2016-2017年上海市上海中学高一上周练09

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上海市上海中学2016-2017学年高一上学期周练(14)数学试题

上海中学高一周练数学卷2016.12.22一. 填空题1. 函数()f x x =--(0)x ≤的反函数是1()f x -=2. 若4log 124x =，则x = 3. 函数2()lg(23)f x x x =--的递减区间是4. 函数21()12f x x =+(2)x <-的反函数是1()f x -= 5. 若函数6,2()3log ,2a x x f x x x -+≤⎧=⎨+>⎩(0a >且1)a ≠的值域是[4,)+∞，则实数a 的取值范围是6. 若函数()8x f x =的图像经过点1(,)3a ，则1(2)f a -+=7. 若函数24,3()(1)1,3x x f x a x x ⎧-≥=⎨-+<⎩存在反函数，则实数a 的取值范围为8. 如果log 41a b =-，则a b +的最小值为9. 若实数t 满足()f t t =-，则称t 是函数()f x 的一个次不动点，设函数()ln f x x =与反函数的所有次不动点之和为m ，则m =10. 设lg lg lg 111()121418x x x f x =+++++，则1()()f x f x+= 11. 设方程24x x +=的根为m ，方程2log 4x x +=的根为n ，则m n +=12. 对区间I 上有定义的函数()g x ，记(){|(),}g I y y g x x I ==∈，已知定义域为[0,3]的函数()y f x =有反函数1()y f x -=，且1([0,1))[1,2)f -=，1((2,4])[0,1)f -=，若方程 ()0f x x -=有解0x ，则0x =二. 选择题13. 如果23499log 3log 4log 5log 100x =⋅⋅⋅⋅⋅⋅⋅，则x ∈（）A. (1,2)B. (2,3)C. (5,6)D. (6,7)14. 函数2x xe e y --=的反函数是（）15. 已知函数()f x 为R 上的单调函数，1()f x -是它的反函数，点(1,3)A -和点(1,1)B 均在函数()f x 的图像上，则不等式1|(2)|1x f -<的解集为（）A. (1,1)-B. (1,3)C. 2(0,log 3)D. 2(1,log 3)16. 设,,0x y z >，且12xyz y z ++=，则422log log log x y z ++的最大值为（）A. 3B. 4C. 5D. 6三. 解答题17. 已知910390x x -⨯+≤，求函数111()4()242x x y -=-+的最大值和最小值；18. 给定实数a ，0a ≠且1a ≠，设函数11x y ax -=-；（1）求证：经过这个函数图像上的任意两个不同的点的直线不平行于x 轴；（2）判断此函数的图像是否关于直线y x =对称，说明你的理由；19. 作出下列函数的大致图像；（1）3|log |||y x =；（2）12log (24)y x =+；20. 设a 是实数，函数()4|2|x xf x a =+-；（1）求证：()f x 不是奇函数；（2）当0a >时，求()f x 的值域；21. 设函数()n n f x x bx c =++，*n N ∈，b 、c R ∈；（1）设2n ≥，1b =，1c =-，证明：()n f x 在区间1(,1)2内存在唯一的零点；（2）设2n =，若对任意12,[1,1]x x ∈-，有2122|()()|4f x f x -≤，求b 的取值范围；参考答案一. 填空题1. 2x -(0)x ≤2.116 3. (,1)-∞- 4. (3)x > 5. (1,2] 6. 237. (1,2] 8. 1 9. 0 10. 3 11. 4 12. 2二. 选择题13. D 14. C 15. C 16. A三. 解答题17. max ()(0)2f x f ==，min ()(1)1f x f ==；18.（1）略；（2）1()()f x f x -=，是； 19. 略；20.（1）略；（2）当102a <<，值域为2[,)a +∞；当12a ≥，值域为1[,)4a -+∞； 21.（1）单调递增，1()02n f <，(1)0n f >；（2）[2,2]-；。

上海市2016_17学年高一数学上学期周练九

上海市2016-2017学年高一数学上学期周练09一. 填空题 1.函数y =的定义域为2. 二次函数221y x x =+-(1)x ≠的值域为3. 若(21)f x -的定义域为(1,2)，则()f x 的定义域为4. 定义域为R 的函数()y f x =的值域为[,]a b ，则函数()y f x c =+的值域为5. 已知函数21ax by x +=+53，则a b += 6.已知函数y =M ，最小值为m ，则mM= 7. 定义运算,,x x y x y y x y≤⎧*=⎨>⎩，若|1||1|m m m -*=-，则m 的取值范围是 8.函数y =的值域为9. 植树节某班20名同学在一段直线公路一侧植树，每人植一棵，相邻两棵树相距10米，开始时需将树苗集中放置在某一树坑旁边，使每位同学从各自树坑出发前来领取树苗往返所走的路程总和最小，这个最小值为10. 若a 是实常数，()f x 对于任何的非零实数x 都有1()()1f af x x x=--，且(1)1f =，则当0x >时，不等式()f x x ≥的解集是11. 已知对任意实数a 、b 满足()()(21)f a b f a b a b -=--+且(0)1f =，则()f x 的函数解析式为12. 将长度为1的铁丝分成两段，分别围成一个正方形和一个圆形，要使正方形与圆的面积之和最小，正方形的周长应为13.设函数()f x =(0)a <的定义域为D ，若所有点(,())s f t (,)s t D ∈构成一个正方形区域，则a =14. 实数集R 中定义运算“*”：（1）对任意,a b R ∈，a b b a *=*；（2）对任意a R ∈， 0a a *=；（3）对任意,a b R ∈，()()()()2a b c c ab a c b c c **=*+*+*-，则函数 1()f x x x=*(0)x >的值域为 15. 设1()|1|f x x =-，22()65f x x x =-+-，函数112212(),()()()(),()()f x f x f xg x f x f x f x ≥⎧=⎨<⎩，若方程()g x a =有四个不同的实数根，则实数a 的取值范围是二. 选择题16. 据统计，一名工人组装第x件产品所用时间（单位：分钟）为()x A f x x A <=≥，A 、c 为常数，已知工人组装第4件产品用时30分钟，组装第A 件产品用时15分钟，那么c 和A 的值分别是（）A. 75，25B. 75，16C. 60，25D. 60，16 17. 已知()y f x =的图像如图所示，则|(2)|1y f x =-+-的图像是（）A. B. C. D.18. 函数2()f x ax bx c =++与2()g x cx bx a =++的值域分别是M 与N ，其中0ac ≠，且a c ≠，则以下结论一定正确的是（）A. M N =B. M N ⊆C. N M ⊆D. M N ≠∅I三. 解答题19. 求下列函数的值域：（1）22256x x y x x -=-+；（2）22124x y x x -=-+(1)x >；20.（1）若()f x 为一次函数，且(23)()2f x f x x ++-=+，求()y f x =的解析式；（2）设3()()1f x xf x=+(0,)x x R ≠∈，求()y f x =的解析式；21. 已知1()2bx f x x a +=+（,a b 是常数，2ab ≠），且1()()f x f k x =；（1）求k 的值；（2）若((1))2kf f =，求,a b 的值；参考答案一. 填空题1. {0}[1,)+∞U2. [2,)-+∞3. (1,3)4. [,]a b5. 4或6.2 7. 1[,)2+∞ 8. [2,)+∞ 9. 2000 10. (0,1] 11. 2()1f x x x =++ 12. 44π+ 13. 4- 14. [3,)+∞ 15. (3,4)二. 选择题16. D 17. C 18. D三. 解答题19.（1）(,2)(2,1)(1,)-∞--+∞U U ；（2）； 20.（1）1()2f x x =-；（2）11()22f x x =--； 21.（1）14k =；（2）7a =-，72b =-；。

上海市上海中学2016-2017学年高一上数学周练08

上海中学高一周练数学卷2016.11.03一. 填空题1. 求出下列不等式的解集：（1）||0a > （2）2103624x x ≤-+< （3）32x x<- （4）25||60x x -+>（5x < （6）22110x x x x --+≤（756x <-2. 已知集合8{|1}2A x x =>+，{|||}B x x a b =-≥，若A B R =，A B =∅，则 a = ，b =3. 若函数12y x b =+的图像与以(1,1)A 、(2,3)B 为端点的线段相交，则常数b 的取值范围是4.在maths 先生的数学班的所有学生中，对于问题“你喜欢数学吗？”在学年开始时，有 50%回答“是”，有50%回答“不”，学年结束时，有70%回答“是”，有30%回答“不”，在全部学生中，有x %的学生在学年开始和结束时给出了不同的回答，则x 的最大值和最小值的差是5. 对任意正数x 和y ，不等式1()()9a x y x y++≥恒成立，则常数a 的取值范围是 6. 令,,,a b c d 是集合{3,2,2,4}--中的不同的元素，则22()()a b c d +++的最大值与最小值之差为7. 关于x 的方程2(2)210x m x m +-+-=有一个根属于(0,1)，则m 取值范围是8. 若||2m ≤时不等式2210mx x m -+-<恒成立，则x 的取值范围是9. 若关于x 的不等式组22202(25)50x x x a x a ⎧--≥⎪⎨+++≤⎪⎩的解集中有且仅有两个整数，则a 的取值范围是10. 函数42321x y x =+的最小值是11. 若正实数a 和b 满足5a b +=的最大值是二. 选择题1.“0.53k <<”是“关于x 的不等式4288(2)50x k x k +-+->的解集为R ”的（） A. 充分不必要条件 B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件2. 若面积为S 的正三角形其外接圆的半径是r ，则（）A. 2S =B. 2S =C. 2S =D. 2S =3. 已知集合{|||1}A x x =<，对任意的a A ∈，B A ∈，则1a b ab ++和1a bab --（）A. 一定都属于AB. 至少有一个属于AC. 至多有一个属于AD.是否属于A 不能确定三. 解答题1. 解关于x 的不等式2(1)10ax a x -++<；2. 求函数y =的定义域和值域；3. 已知非空集合M R ⊆，定义域为R 的函数1,()0,M x M f x x M ∈⎧=⎨∉⎩，若A 、B 是R 的两个非空真子集，试求函数()1()()()1A B A B f x F x f x f x +=++的值域；4. 列车提速可以提高铁路运输量，但并非列车速度越大，列车的流量Q （单位时间内通过观测点的列车数量）就越大，因为列车运行时，前后两车必须要保持一个“安全间隔”，“安全间隔”与列车的速度v 的平方成正比（比例系数0k 为定值，00k >），假设所有的列车长度均为l ，问：列车车速多大时，列车的流量Q 最大；5. 已知0x y >>y x >；参考答案一. 填空题1.（1）(,1)(1,)-∞-+∞ （2）(3,1][4,6)-- （3）(2,)+∞ （4）(,3)(2,2)(3,)-∞--+∞ （5）R （6）{1} （7）36(,)25+∞ 2. 2a =，4b = 3. 1[,2]24. 605. [4,)+∞6. 607. 1(,62-8. 11(22-++ 9. (2,1][4,5)- 10. 011.二. 选择题 1. A 2. C 3. A三. 解答题1. 当0a <，1(,)(1,)x a ∈-∞+∞；当0a =，(1,)x ∈+∞；当01a <<，1(1,)x a∈；当1a =，x ∈∅；当1a >，1(,1)x a ∈；2. 定义域：[1,2)(2,)+∞，值域：(,8](0,)-∞-+∞； 3. 2{,1}3； 4. 20v Q l k v =+，v =Q 最大； 5. 略；。

上海市2016_2017学年高一数学上学期周练012017092204109

上海市 2016-2017学年高一数学上学期周练 01一. 填空题1. 用恰当的符号填空：（1） 2 R ；（2） 4 2 3 {1, 2, 3 1}；（3） (1,1){(x , y ) | yx 2}；（4）{x | 2x 2 3x 2 0}Q ；2. 已知全集U {0,1, 2,3, 4,5, 6, 7,8,9}，集合 A {0,1, 3, 5, 8}，集合 B{2, 4,5, 6,8}，则 (C A )(C B )UU3. 已知集合 P {x | x 21}， M{a }，若 P MP ，则 a 的取值范围是4. 已知集合 A{x || x 2 |3}，集合 B {x | (x m )(x 2) 0}，且A B {x | 1 x n }mn，则，5. 已知集合 A {1, 2,3}， B {2, 4, 5}，则集合 AB 的子集的个数为 6. 设 M{x | y 2 x 2}， N{x | y 22x8}，则 MN7. 已知非空集合 S N * ，满足条件“若 xS ，则16 S ”，则集合的个数是S x8. 已知集合 A {(x , y ) | y x 2}，{( , ) | 1 1}，则B x yyA B9. 用| S |表示集合 S 中元素的个数，设 A , B ,C 为集合，称 (A , B ,C ) 为有序三元组，如果集合 A , B ,C 满足| AB | | BC | | C A | 1，且 A B C，则称有序三元组(A , B ,C ) {1, 2,3, 4}为最小相交，由集合的子集构成的所有有序三元组中，最小相交的有序三元组的个数为 10. 设 M{1, 2, 3,, 2024, 2025}， A 是 M 的子集且满足：当 x A 时，15x A ，则 A中元素最多有个11.设集合 A{1, 2, 3,,1000}，若 B且 B A ，记G (B ) 为 B 中元素的最大值与最小值之和，则对所有的 B ，G (B ) 的平均值为二. 选择题 12. 设集合U {1, 2,3, 4,5, 6}， M{1, 2, 4}，则C M（）UA. UB. {1, 3, 5}C. {3, 5, 6}D. {2, 4, 6}13. 现有以下四个判断：- 1 -（1）{质数}{奇数}；（2）集合{1,2,3}与集合{4,5,6}没有相同的子集；（3）空集是任何集合的真子集；（4）若A B，B C，则A C；其中，正确的判断的个数为（）A. 0B. 1C. 2D. 314. 下列表示图形中的阴影部分的是（）A. (A C)(B C)B. (A B)(A C)C. (A B)(B C)D. (A B)C15. 满足a,b{1,0,1,2}，且关于x的方程ax22x b0有实数解的有序数对(a,b)的个数为（）A. 14B. 13C. 12D. 1016. 若集合E{(p,q,r,s)|0p s4,0q s4,0r s4且p,q,r,s N}，F{(t,u,v,w)|0t u4,0v w4t,u,v,w N}card(X)X且，用表示集合中的元素个数，则card(E)card(F)（）A. 50B. 100C. 150D. 200三. 解答题17. 已知集合A{x|x25x60}，B{x|mx10}，且A B A，求实数m；18. 已知集合A{m|m n21,n N*}，B{y|y x22x2,x N*}，探究A、B 之间的关系，并证明你的结论；- 2 -19. 设，若，则称A{a,a,a,,a}M(n N*,n2)a a a a aa A123n12n12n为集合M的n元“好集”；（1）写出实数集R的一个二元“好集”；（2）问：正整数集N*上是否存在二元“好集”？说明理由；（3）求出正整数集N*上的所有“好集”；参考答案一. 填空题1. 、、、2. {7,9}3. [1,1]4. 1、15. 326. [2,4]7. 78. {(1,1)}9. 10. 11.961899100124- 3 -二. 选择题 12. C13. B14. A15. B16. D三. 解答题m1 1A B17.或或；18. 真包含于；2 3119.（1）；（2）不存在；（3）；{1, }{1, 2, 3}2- 4 -。

上海市2016_2017学年高一数学上学期周练082017092204115

上海市 2016-2017学年高一数学上学期周练 08一. 填空题1. 求出下列不等式的解集： 1 （1）（2）| a |10 x 2 3x 6 24a 23（3）（4） x2 xx 2 5| x | 6 011 （5） x 21 4x2 2 x （6） x 2xx x20 （7） x 5x 682. 已知集合，，若，，则A{x | 1} B {x || x a | b } A B R A Bx 2 ab，1 3. 若函数的图像与以、为端点的线段相交，则常数的取值范围yx b A (1, 1) B (2, 3) b2是4.在 maths 先生的数学班的所有学生中，对于问题“你喜欢数学吗？”在学年开始时，有 50%回答“是”，有 50%回答“不”，学年结束时，有 70%回答“是”，有 30%回答“不”，在全部学生中，有 x %的学生在学年开始和结束时给出了不同的回答，则 x 的最大值和最小值的差是1 a5. 对任意正数 x 和 y ，不等式 (x y )( ) 9 恒成立，则常数 a 的取值范围是x y6. 令 a ,b ,c ,d 是集合{3,2, 2, 4}中的不同的元素，则 (a b )2 (c d )2 的最大值与最小值之差为7. 关于 x 的方程 x 2 (m 2)x 2m10有一个根属于 (0,1) ，则 m 取值范围是8. 若| m |2时不等式 mx 22x 1m0恒成立，则 x 的取值范围是2xx 2 09. 若关于 x 的不等式组的解集中有且仅有两个整数，则的取值a22x(2a5)x5a0范围是3x410. 函数的最小值是y2x1211. 若正实数a和b满足a b5，则a1b3的最大值是- 1 -二. 选择题1.“0.5k3”是“关于x的不等式8x48(k2)x25k0的解集为R”的（）A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件2. 若面积为S的正三角形其外接圆的半径是r，则（）A. S3r2B. S3r2C. 33D.S r S3r2424a b a b3. 已知集合A{x||x|1}，对任意的a A，B A，则和（）1ab1abA. 一定都属于AB. 至少有一个属于AC. 至多有一个属于AD. 是否属于A不能确定三. 解答题1. 解关于x的不等式ax2(a1)x10；92. 求函数的定义域和值域；y2x3x1- 2 -1,x Mf(x)3. 已知非空集合M R，定义域为R的函数，若A、B是R的两个M0,x Mf(x)1F(x)A B非空真子集，试求函数的值域；f(x)f(x)1A B4. 列车提速可以提高铁路运输量，但并非列车速度越大，列车的流量Q（单位时间内通过观测点的列车数量）就越大，因为列车运行时，前后两车必须要保持一个“安全间隔”，“安全间隔”与列车的速度v的平方成正比（比例系数为定值，00），假设所有的列车长kk度均为l，问：列车车速多大时，列车的流量Q最大；5. 已知x y0，证明y21y x21x；- 3 -参考答案一. 填空题 1.（1） (,1) (1,) （2） (3,1][4, 6) （3）(2,)（4） (,3) (2, 2) (3,) （5） R（6）{1} （7） (36 ,)252. a2 ，b 4 3. [1 ,2]4. 5. 6.60[4,) 6021(1 7 ,13)7.8.9.( ,6 2 7] 222(2,1][4,5)10. 0 11. 3 2二. 选择题 1. A2. C3. A三. 解答题 1. 当 a0 ， x(, 1) (1,) ；当 a 0 ， x (1,) ；当 0 a1， x (1, 1) ；aa当 a1，x ；当 a1， x (1 ,1) ；a 2. 定义域：[1, 2)(2,) ，值域： (,8] (0,) ；23.；{ , 1} 3vl 4.，时，最大；QvQl k vk2 05. 略；- 4 -。

上海市上海中学2016-2017学年高一上学期周练(12)数学试题Word版含答案

上海中学2019届高一数学周练十二2016.12.08一. 填空题1. 幂函数23y x -=的定义域为，值域为2. 定义在[4,4]-上的偶函数()g x 满足：当0x ≤时，()g x 单调递增，若(1)()g m g m -<，则m 的取值范围是3. 若函数2()|21|f x x x a a =++-+的图像关于y 轴对称，则实数a =4. 若函数()y f x =是定义在(0,)+∞上的减函数，则函数2(2)y f x x =-的单调递增区间是5. 已知点(,)A a b ()a b ≠位于直角坐标平面的第一象限，点A 以及点A 关于直线y x =的对称点B 都在一个幂函数()y f x =的图像上，则()f x =6. 设函数()y f x =对一切实数x 均满足(5)(5)f x f x +=-，且方程()0f x =恰有7个不同的实根，则这7个实根的和为7. 已知函数()||f x x a x b =-+，给出下列命题：（1）当0a =时，()f x 的图像关于点(0,)b 成中心对称；（2）当(,)x a ∈+∞时，()f x 是递增函数；（3）当0x a ≤≤时，()f x 的最大值为24a b +，其中正确的序号是 8. 已知函数()y f x =是R 上的增函数，则0a b +>是()()()()f a f b f a f b +>-+-的条件9. 函数(2)y f x =+的图像过点(1,3)-，则函数()y f x =的图像关于x 轴对称的图像一定经过点10. 函数122010()1232011x x x x f x x x x x +++=+++⋅⋅⋅+++++的图像的对称中心为 11. 设函数1()f x x x =+的图像为1C ，1C 关于点(2,1)A 对称的图像为2C ，2C 对应的函数为()g x ，则()g x 的解析式为12. 若函数()f x 满足(||)|()|f x f x =，则称()f x 为对等函数，给出以下三个命题：（1）定义域为R 的对等函数，其图像一定过原点（2）两个定义域相同的对等函数的乘积一定是对等函数（3）若定义域是D 的函数()y f x =是对等函数，则{|(),}{|0}y y f x x D y y =∈⊆≥其中真命题的个数是二. 选择题13. 幂函数223()(1)m m f x m m x +-=--在(0,)+∞上是减函数，则实数m =（）A. 2或1-B. 1-C. 2D. 2-或114. 已知函数:f R R →，则对所有实数x ，满足221()(())4f x f x -≥，且对不同的x ， ()f x 也不同，这样的函数()f x （）A. 不存在B. 有限多个C. 唯一存在D. 无穷多个15. 函数()y f x =的定义域和值域都是(,0)-∞，则()y f x =-的图像一定位于（）A. 第一象限B. 第二象限C. 第三象限D. 第四象限16. 已知集合{()|()A f x f x =是幂函数且为奇函数}，集合{()|()B f x f x =是幂函数且在R 上单调递增}，集合{()|()C f x f x =是幂函数且图像过原点}，则（）A. A B C =B. B A C =C. C A B =D. A B C =17. 定义域和值域均为[,]a a -（常数0a >）的函数()y f x =和()y g x =的图像如图所示，给出下列四个命题：（1）方程(())0f g x =有且仅有三个解；（2）方程(())0g f x =有且仅有三个解；（3）方程(())0f f x =有且仅有九个解；（4）方程(())0g g x =有且仅有一个解；那么，其中正确命题的个数是（）A. 4B. 3C. 2D. 1三. 解答题18. 画出下列函数图像：（1）34y x =；（2）2y x -=；19. 若函数34220()(42)(1)f x mx x m x mx -=++++-+的定义域为R ，求实数m 的范围；20. 已知函数22()k k f x x -++=()k Z ∈满足(2)(3)f f <；（1）求k 的值并求出相应的()f x 的解析式；（2）对于（1）中的()f x ，试判断是否存在q (0)q >，使函数()1()(21)g x qf x q x =-+- 在区间[1,2]-上的值域为17[4,]8-？若存在，求出q ；若不存在，请说明理由；21. 已知函数()f x = （1）求函数()f x 的定义域和值域；（2）若00()f x x =，求0x 的值；参考答案一. 填空题1. (,0)(0,)-∞+∞，(0,)+∞ 2. 1[3,)2- 3. 12 4. (,0)-∞ 5. 1x - 6. 35 7. （1）（3） 8. 充要 9. (1,3)-10. (1006,2011)- 11. 1()24g x x x =-+- 12. 1二. 选择题13. B 14. A 15. D 16. B 17. C三. 解答题18. 略；19. 1,2)；20.（1）0k =或1，2()f x x =；（2）2q =；21.（1）定义域[1,0)[1,)-+∞，值域[0,)+∞；（2；。

2016-2017年上海市上海中学高一上周练12

上海中学高一周练数学卷2016.12.08一. 填空题1. 幂函数23y x -=的定义域为，值域为2. 定义在[4,4]-上的偶函数()g x 满足：当0x ≤时，()g x 单调递增，若(1)()g m g m -<，则m 的取值范围是3. 若函数2()|21|f x x x a a =++-+的图像关于y 轴对称，则实数a =4. 若函数()y f x =是定义在(0,)+∞上的减函数，则函数2(2)y f x x =-的单调递增区间是5. 已知点(,)A a b ()a b ≠位于直角坐标平面的第一象限，点A 以及点A 关于直线y x =的对称点B 都在一个幂函数()y f x =的图像上，则()f x =6. 设函数()y f x =对一切实数x 均满足(5)(5)f x f x +=-，且方程()0f x =恰有7个不同的实根，则这7个实根的和为7. 已知函数()||f x x a x b =-+，给出下列命题：（1）当0a =时，()f x 的图像关于点(0,)b 成中心对称；（2）当(,)x a ∈+∞时，()f x 是递增函数；（3）当0x a ≤≤时，()f x 的最大值为24a b +，其中正确的序号是 8. 已知函数()y f x =是R 上的增函数，则0a b +>是()()()()f a f b f a f b +>-+-的条件9. 函数(2)y f x =+的图像过点(1,3)-，则函数()y f x =的图像关于x 轴对称的图像一定经过点10. 函数122010()1232011x x x x f x x x x x +++=+++⋅⋅⋅+++++的图像的对称中心为 11. 设函数1()f x x x=+的图像为1C ，1C 关于点(2,1)A 对称的图像为2C ，2C 对应的函数为()g x ，则()g x 的解析式为 12. 若函数()f x 满足(||)|()|f x f x =，则称()f x 为对等函数，给出以下三个命题：（1）定义域为R 的对等函数，其图像一定过原点（2）两个定义域相同的对等函数的乘积一定是对等函数（3）若定义域是D 的函数()y f x =是对等函数，则{|(),}{|0}y y f x x D y y =∈⊆≥ 其中真命题的个数是二. 选择题13. 幂函数223()(1)m m f x m m x +-=--在(0,)+∞上是减函数，则实数m =（）A. 2或1-B. 1-C. 2D. 2-或114. 已知函数:f R R →，则对所有实数x ，满足221()(())4f x f x -≥，且对不同的x ， ()f x 也不同，这样的函数()f x （）A. 不存在B. 有限多个C. 唯一存在D. 无穷多个15. 函数()y f x =的定义域和值域都是(,0)-∞，则()y f x =-的图像一定位于（）A. 第一象限B. 第二象限C. 第三象限D. 第四象限16. 已知集合{()|()A f x f x =是幂函数且为奇函数}，集合{()|()B f x f x =是幂函数且在R 上单调递增}，集合{()|()C f x f x =是幂函数且图像过原点}，则（）A. A B C =IB. B A C =IC. C A B =ID. A B C =U17. 定义域和值域均为[,]a a -（常数0a >）的函数()y f x =和()y g x =的图像如图所示，给出下列四个命题：（1）方程(())0f g x =有且仅有三个解；（2）方程(())0g f x =有且仅有三个解；（3）方程(())0f f x =有且仅有九个解；（4）方程(())0g g x =有且仅有一个解；那么，其中正确命题的个数是（）A. 4B. 3C. 2D. 1三. 解答题18. 画出下列函数图像：（1）34y x =；（2）2y x -=；19. 若函数34220()(42)(1)f x mx x m x mx -=++++-+的定义域为R ，求实数m 的范围；20. 已知函数22()k k f x x -++=()k Z ∈满足(2)(3)f f <；（1）求k 的值并求出相应的()f x 的解析式；（2）对于（1）中的()f x ，试判断是否存在q (0)q >，使函数()1()(21)g x qf x q x =-+- 在区间[1,2]-上的值域为17[4,]8-？若存在，求出q ；若不存在，请说明理由；21. 已知函数()f x =；（1）求函数()f x 的定义域和值域；（2）若00()f x x =，求0x 的值；参考答案一. 填空题1. (,0)(0,)-∞+∞U ，(0,)+∞2. 1[3,)2-3. 124. (,0)-∞5. 1x -6. 357. （1）（3）8. 充要9. (1,3)-10. (1006,2011)- 11. 1()24g x x x =-+- 12. 1二. 选择题13. B 14. A 15. D 16. B 17. C三. 解答题18. 略；19. 1,2)；20.（1）0k =或1，2()f x x =；（2）2q =；21.（1）定义域[1,0)[1,)-+∞U ，值域[0,)+∞；（2）12；。

上海上海中学高一上学期周练英语试题

上海上海中学高一上学期周练英语试题集团标准化办公室：[VV986T-J682P28-JP266L8-68PNN]上海中学2017-2018学年第学期高一英语试题Choice21.The impact__________ high technology draws worldwide attention.A.onB.toC.ofD.in22.________________,the more expansive gestures you should employ when youdeliver a speech.A.The more audience there isB.The more the audience areC.As much audience as there isD.The larger the audience is23.John is really an independent boy and he tries his best to settle everyproblem_______.A.of his ownB.by his own C,for his own D.on his own24.The queen,__________ an old woman, made a poisonous apple and came tothe cottage to tempt Snow White to eat it.A,dressed in B.who was dressing like C.dressed like D.who had clotheson as25.It is reported that __________schools in the west of China are improvingtheir study environment.A.a great many ofB.the large number ofB..a great amount of D.a large number of26.Do you really mean_________a basketball player? Do you know thattraining to be a basketball player means_____________at least eight hoursevery day?A.being,practicingB.to be,practicingC.to be,to practiceD.being,topractice27.Balancing the workload of a _________job alongside a course of study can be difficult, so there is an increasing tendency for people to give up work and go back to school.A.demandingB.rewardingC.leadingD.outstanding28. I couldn’t re sist having another piece of cake ____________I was supposed to be on a diet and lose weight.A.untilB.wheneverC.asD.even if29. Your children will not follow your advice to ____________business management as his major if you ___________.A.take up,force him toB.take up,force himC.take on,force him toD.take on,force him30.The students of class 8____________a farewell party for their retired class teacher from then on.A.made a great decision to holdingB.made up their mind to holdC.were determined to holdD.decide to hold31.The machine is easy to___________，___________is shown in the pictures.A.operate on, whichB.be operated, whichC.be operated on, asD.operate, as32.Mary’s talent for music and acting led her into a(n)_________on the stage.A.workB.professionC.occupationD.career33.Although the old man insisted he ___________all right,his children all insisted he______________to hospital at once.A.was,would be sentB.was, be sentC.be,would be sentD.be,be sent34.It was the financial scandal that he was involved___________pushed him to give up his political career.A.that B，in what C.in that D. in whichans are parts of our body,____________a special function to perform.A.each of them has B,each has C.every of which has D.each of which has36.A;It will be the first time that I _____________the subject.B;Don’t worry.It will be a little difficult the first time you_________it.A.have taught,teachB.teach,have taughtC.will teach,will teachD.have taught,will teach37.Slipping off the bicycle an getting hurt,Jack asked a pass-by whether there was a drugstore around________he could buy the medicine for his broken knee,A.whereB.whenC.whichD.that38.I have a house,________ the southA.that window opensB.of which the window opens toC.whose window open toD.the windows of which opens39.E-mail is a convenient, highly informal medium for conveying message among people __________well satisfies human needs.A.what B,who C.that D.for which40.According to a report recently released by the US National Research Council,the amount of space junk flowing in Earth’s orbit has reached a critical lever_________future space mission may become too dangerous to fly.A.thatB.whereC.whose D of which41.Marco Polo,who was a great Italian traveler, traveled all the way to China,_________was then called Cathy.A.whereB.whichC.whenD.what42.He arrived in New York in 1986,____________some time later, he became a writer.A.whenB.whereC.thatD.which43.It was almost midnight_________the ceremony was over.A.thatB.sinceC.when D,till44.Jenny smiled________her mother did when she was Jenny’s age.A.whatB.whereC.thatD.which45._________did you use to do________you don’t do now?A.46._______glitters is not gold not all those__________wander are lost.A.What,whoB.All that,whoC.All,thatD.What,that47.Sparking Lake in Jiuzhaigou is so beautiful a place_________people can memorize forever even it no longer exists in real life.A.thatB.whichC.asD.what48.I sent invitation to 100people to the party,__________turned up.A.of whom only a thirdB.only 30 of theseC.almost all of themD.and none of them49.There is no difficulty___________we can overcome.A.whichB.thatC.whatD.but50.Could you lend me a knife________?A.which to open the canB.with which to open a canC.with which I opened the canD.with which I can use to open a canVocabularyComplete the following passage by using the words in the box.Each word can only be used once. Note that there is one word more than you need.Prederic Mishikn, who’s been a professor at Columbia Business School for almost 30 years, is good at solving problems and expressing ideas. Whether he’s sending in front of a lecture hall or engaged in a ____51______ conversion, his hands are always waving and pointing. When he was in_____52_______school,one of his professors was so annoyed bythis____53_____gesturing that he made the young economist sit on his hands whenever he visited the professor’s office.I t turns out, however, that Mishikn’s professor had it exactly wrong. Gesture doesn’t prevent but ____54_____clear thought and speech.Research______55____that the movements we make with our hands when wetalk_______56_____a kind of second language, adding information that is____57_______from our words. It is learning’s_____58_______code;Gestures reveals what we know. It also reveals what we don’t know. What’s more, the agreement(or______59_______of agreement)between what our voices say and how our hands move offers a ___60________to our readiness to learn.III. Reading ComprehensionSection ADirections:?For each blank in the following passage there are fourwords?or?phrases?marked A,?B,?C and D. Fill in each blank with the word or phrase that best fits the?context.One of the big excuses for not learning languages in Britain is that when you try them out abroad, the person you are speaking to responds in__61__ English, making you feel about two feet tall—or should that be 36 cm?English people are known for their reluctance to accept changes leading to closer union with us European partners. __62__ according to organizations promoting English business, ____63_____language learning is concerned, that simply doesn’t __53__ in that 21st?century.Trade Section UK aims to help British companies trading overseas. Its chief executive, Sir David Wright, says: “Language __64__ are good for business, good for jobs and help people in their career. Although many people may speak English __65__, they will usually negotiate in their own language. If we are to compete on an equal basis, it’s decisive that business ______66____ the challenge and uses languages more effectively.”The Council of Europe __67__ language learning as an important tool to improve communication and mutual understanding between individuals. The Center for Information on Language Teaching says that being able to speak __68__ language is a “basic life skill” and that the “language deficit in the UK has become an urgent economic, __69__ and political question.”The department for Education and Skills wants to __70__ teaching of modern foreign languages (MFT) at an earlier stage in the future. Primary school children will get greater __71__?to foreign language learning. Currently, about 20 percent of primary schools offer MFL teaching. The Department wants to increase this __72__ by 2012 every child has an entitlement to study a language at primary school.Education and Skills secretary Estelle Morris is very __73__ about more primary schools taking up the __74__ challenge. Children are just so much more responsive___75_____an earlier age.61. A. broken B. perfect C. natural D. simple62. A. And B. But C. So D. Besides63. A. whose B. where C. which D. that64. A. technology B. Learners C. skills D. teachers65. A. at home B. in school C aboard D. Overseas66. A. takes up B. takes off C. takes over D. takes in67. A. finds B. thinks C. regards D. believes68. A. native B. local C. another D. certain69. A. physical B. mental C. spiritual D. social70. A. permit B. encourage C. demand D. challenge71. A. admission B. access C. chance D. approach72. A. in that B. that C. now that D. so that73. A. worried B. concerned C. positive D. negative74. A. language B. business C. competition D. learning75. A. to B. on C. at D. ofReading comprehension(A)I made a pledge (发誓) to myself on the way down to the vacation beach cottage. For two weeks I would try to be a loving husband and father. Totally loving. No ifs, ands or buts.The idea had come to me as I listened to a talk on my car radio. The speaker was quoting a Biblical (圣经的) passage about husbands being thoughtful of their wives. Then he went on to say, "Love is an act ofwill.A person can choose to love." To myself, I had to admit that I had been a selfish husband. Well, for two weeks that would change.And it did. Right from the moment I kissed Evelyn at the door and said, "That new yellow sweater looks great on you."Oh, Tom, you noticed," she said, surprised and pleased, maybe a little puzzled.After the long drive, I wanted to sit and read. Evelyn suggested a walk on the beach. I started to refuse, but then I thought, "Evelyn's been alone here with the kids all the week and now she wants to stay with me." We walked on the beach while the children flew their kites.So it went. Two weeks of not calling the Wall Street firm where I am a director; a visit to the shell museum though I usually hate museums. Relaxed and happy, that's how the whole vacation passed. I made a new pledge to keep on remembering to choose love.There was one thing that went wrong with my experiment, however. Evelyn and I still laugh about it today.Last night at our cottage, preparing for bed, Evelyn stared at me with the saddest expression." What's the matter?" I asked her."Tom," she said in a voice filled with distress, "do you know something I don't?""What do you mean?"" Well...that checkup (体检) I had several weeks ago...our doctor (i)he tell you something about me?Tom, you've been so good to me...am I dying?"It took a moment for it all to sink in. Then I burst out laughing."No, honey," I said, wrapping her in my arms. "You're not dying; I'm just starting to live."76. In the first paragraph, "No ifs, ands or buts" probably means ____.A. UnnecessarilyB. unconditionallyC. impossiblyD. unexpectedly77. During the two weeks on the beach, Tom showed more love to his wife because _____.A. she looked lovely in her new clothesB. she was seriously illC. he was determined to be a good husbandD. he had made a lot of money in Wall Street78.By saying "I'm just starting to live", Tom means that _____.A. he is beginning to feel regretful for what he did to his wifeB. he lived an unhappy life before and is now starting to changeC. he is just beginning to understand the real meaning of lifeD. he is just beginning to enjoy his life as a loving husband(B)As I was thinking about language learning the other day, the image of baking bread came into my mind．I compared some of the exercises and drills that we put ourselves through in order to learn a language to the various ingredients (原料) that go into baking a loaf of fresh bread．Real language learning takes place in human relationships．No one sits down and eats a cup of flour, even if he is hungry and in a hurry．You don' t become bilingual (双语的) by learning lists of vocabulary．You don' tbecome a speaker of a language by memorizing grammatical rules．You become bilingual by entering a community that uses that other language as its basic means of communication．I am not suggesting that we can make bread without ingredients．Flour is necessary, as are yeast (酵母), salt, water and other ingredients．Vocabulary is part of any language and will have to be learned．Grammatical rules exist in every language and cannot be ignored．But merely combining the appropriate ingredients in the recommended proportions does not result in bread．At best, you only end up with a ball of dough (面团)．In order to get bread, you have to apply heat to the dough．And in language learning, that heat comes from the community．Anyone who has learned a second language has experienced that heat．It creeps up your neck when you ask the babysitter “Have you already been eaten?” when you meant to say, ‘‘Have you already eaten?” When you try to sa y something quite innocent and the whole room bursts into laughter, you are experiencing the heat that turns raw dough into good bread．Remember the old saying, “If you can' t stand the heat, get out of the kitchen"．This is where language learning often breaks down because we find the heat uncomfortable and we stop the baking process．In other words, we can' t stand the heat, so we get out of the kitchen．However, the language learner who stays in the kitchen－in the heat－until the combined ingredients are thoroughly transformed will enjoy the richness of a quality loaf of bread. He is glad that he did not "get out of the kitchen” at the important moment when the oven seemed too hot.The dedicated language learner knows that becoming bilingual cannot be achieved without the heat.79.According to the author, you can possibly become a speaker of a language by ________．A．bearing millions of words and expressions in your mindB．using the language to communicate with those around youC．Knowing verb conjugations and grammatical rulesD．saying something innocent to be laughed at by others80.'What’s the purpose of illustration of the example-you ask the babysitter,"Have you already been eaten?"When you meant to say,"Have you already eaten?"?A. To verify that you are sure to make some mistakes when you enter a community.B.To show that you should combine the ingredients in the recommended proportions.C. To prove that you may experience"heat"from the community in language learning.D. To indicate that being bilingual calls for your courage, confidence and perseverance.81.According to the passage, which of the following is NOT the necessity of baking bread and learning language?A．Excellent Skills．B．Various ingredients．C．Appropriate proportions．D．Uncomfortable heat．(C)Like most people, I’ve long understood that I’ll be judged by my occupation, that my profession is used by people to see how talented I am. Recently, however, I was disappointed to see that it also decides how I’m treated as a person.Last year I left a professional position as a small-town reporter and took a job waiting tables. As someone paid to serve food to people, I had customers say and do things to me I suppose they’d never say or do to the people they know. One night a man talking on his cell phone waved me away,then called me back with his finger a minute later, saying angrily that he was ready to order and asking where I’d been.I had waited tables during summers in college and was treated like a peon（勤杂工） by plenty of people. But at 19 years old, I believed I deserved inferior（低等的）treatment from professional adults. Besides, people responded to me differently after I told them I was in college. Customers would joke that one day I’d be sitting at their table, waiting to be served.Once I graduated I took a job at a community newspaper. From my first day, I heard a respectful tone from everyone who called me. I assumed this was the way the professional world worked--- politely and formally.I soon found out differently. I sat several feet away from a person in advertising department with a similar name. Our calls would often get mixed up and someone asking for Kristen would be transferred to Christie. The mistake was immediately clear. Perhaps it was because of money, but people used a tone with Kristen that they never used with me.My job title made people treat me with courtesy. So it was a shock to return to be the restaurant industry.It’s no secret that there’s a lot to put up with when waiting tables, and fortunately, much of it can be easily forgotten when you pocket the tips. The service industry exists to meet others’ needs. Still, it seemed that many of my customers didn’t get the difference between server and servant.I’m now applying to graduate school, which means someday I’ll return to a profession where people need to be nice to me in order to get what they want. I think I’ll take them to dinner first, and see how they treat someone whose job is to serve them.82.The author was disappointed to find that_____________？A. one’s position is used to measure one’s intelligence.B. Talented people like her should fail to get a respectable jobC. one’s occupation affects the way one is treated as a person.D. professionals tend to look down upon manual workers.83. What does the author intend to say by the example in Paragraph 2？A. Waiting tables is a hard job.B. Some customers are difficult to deal with.C. The man making a phone call is absent-minded.D. Some customers show no respect to those who serve them.84.What does the author imply by saying"... Many of my customers didn’t get the difference between server and servant (Lines 3-4, Para. 7)?A. Those who cater to others' needs are destined to be looked down upon.B. Those working in the service industry shouldn't be heated as servants.C. Those serving others have to put up with rough treatment to earn a living.D. The majority of customers tend to look on a servant as 4. server nowadays.85. The author says one day she’ll take her customers to dinner in order to _______.A. see what kind of person they areB. experience the feeling of being servedC. shoe her generosity towards people inferior to herD.arouse their sympathy for people living a humble life(D)In 1784, five years before he became president of the United States, George Washington, 52, was nearly toothless. So he hired a dentist to transplant nine teeth into his jaw—having extracted them from the mouths of his slaves.That's a far different image from the cherry-tree-chopping George most people remember from their history books. But recently, many historians have begun to focus on the roles slavery played in the lives of the founding generation. They have been spurred in part by DNA evidence madeavailable in 1998, which almost certainly proved Thomas Jefferson had fathered at least one child with his slave Sally Hemings. And only over the past 30 years have scholars examined history from the bottom up. Works of several historians reveal the moral compromises made by the nation's early leaders and the fragile nature of the country's infancy. More significantly, they argue that many of the Founding Fathers knew slavery was wrong—andyet most did little to fight it.More than anything, the historians say, the founders were hampered bythe culture of their time. While Washington and Jefferson privately expressed distaste for slavery, they also understood that it was part ofthe political and economic bedrock of the country they helped to create.For one thing, the South could not afford to part with its slaves. Owning slaves was "like having a large bank account," says Wiencek, authorof An Imperfect God: George Washington, His Slaves, and the Creation of America. 'The southern states would not have signed the Constitutionwithout protections for the "peculiar institution," including a clause that counted a slave as three fifths of a man for purposes of congressional representation.And the statesmen's political lives depended on slavery. The three-fifths formula handed Jefferson his narrow victory in the presidential election of 1800 by inflating the votes of the southern states in the Electoral College. Once in office, Jefferson extended slavery with the Louisiana Purchase in 1803; the new land was carved into 13 states,including three slave states.Still, Jefferson freed Hemings' children—though not Hemings herself or his approximately 150 other slaves. Washington, who had begun to believethat all men were created equal after observing the bravery of the black soldiers during the Revolutionary War, overcame the strong opposition ofhis relatives to grant his slaves their freedom in his will. Only a decade earlier, such an act would have required legislative approval in Virginia.86. In Paragraph 1,George Washington's dental surgery is mentionedto__________A．show the poor medical practice in the past.B．demonstrate the great cruelty of slavery in his days.C．stress the important role of slaves in the entire U.S. history. D．reveal an unknown aspect of his life and introduce the topic87.We may infer from the second paragraph that_____________.A. DNA technology has been widely applied to history research.B. In its early day. s the U. S. was confronted with delicate situations.C. historians deliberately made up some stories of Jefferson's life.D.Political compromises are easily found throughout the U. S. history.88. What do we learn about Thomas Jefferson?A. His political view changed his attitude towards slavery.B. His status as a father made him free the child slaves.C. His attitude towards slavery was complex.D. His affair with a slave ruined his reputation.89.Which of the following is TRUE according to the text?A. Some founding fathers benefited politically from slavery.B. Slaves in the old days did not have the right to vote.C. Slave owners usually had large savings accounts.D. Washington decided to free slaves due to moral considerations. Translation1.社会上，年轻人赶时髦，穿时尚衣服是常有的事。

上海上海中学高一上学期周练英语试题完整版

上海上海中学高一上学期周练英语试题集团标准化办公室：[VV986T-J682P28-JP266L8-68PNN]上海中学2017-2018学年第学期高一英语试题Choice21.The impact__________ high technology draws worldwide attention.A.onB.toC.ofD.in22.________________,the more expansive gestures you should employ when youdeliver a speech.A.The more audience there isB.The more the audience areC.As much audience as there isD.The larger the audience is23.John is really an independent boy and he tries his best to settle everyproblem_______.A.of his ownB.by his own C,for his own D.on his own24.The queen,__________ an old woman, made a poisonous apple and came tothe cottage to tempt Snow White to eat it.A,dressed in B.who was dressing like C.dressed like D.who had clotheson as25.It is reported that __________schools in the west of China are improvingtheir study environment.A.a great many ofB.the large number ofB..a great amount of D.a large number of26.Do you really mean_________a basketball player? Do you know thattraining to be a basketball player means_____________at least eight hoursevery day?A.being,practicingB.to be,practicingC.to be,to practiceD.being,topractice27.Balancing the workload of a _________job alongside a course of study can be difficult, so there is an increasing tendency for people to give up work and go back to school.A.demandingB.rewardingC.leadingD.outstanding28. I couldn’t re sist having another piece of cake ____________I was supposed to be on a diet and lose weight.A.untilB.wheneverC.asD.even if29. Your children will not follow your advice to ____________business management as his major if you ___________.A.take up,force him toB.take up,force himC.take on,force him toD.take on,force him30.The students of class 8____________a farewell party for their retired class teacher from then on.A.made a great decision to holdingB.made up their mind to holdC.were determined to holdD.decide to hold31.The machine is easy to___________，___________is shown in the pictures.A.operate on, whichB.be operated, whichC.be operated on, asD.operate, as32.Mary’s talent for music and acting led her into a(n)_________on the stage.A.workB.professionC.occupationD.career33.Although the old man insisted he ___________all right,his children all insisted he______________to hospital at once.A.was,would be sentB.was, be sentC.be,would be sentD.be,be sent34.It was the financial scandal that he was involved___________pushed him to give up his political career.A.that B，in what C.in that D. in whichans are parts of our body,____________a special function to perform.A.each of them has B,each has C.every of which has D.each of which has36.A;It will be the first time that I _____________the subject.B;Don’t worry.It will be a little difficult the first time you_________it.A.have taught,teachB.teach,have taughtC.will teach,will teachD.have taught,will teach37.Slipping off the bicycle an getting hurt,Jack asked a pass-by whether there was a drugstore around________he could buy the medicine for his broken knee,A.whereB.whenC.whichD.that38.I have a house,________ the southA.that window opensB.of which the window opens toC.whose window open toD.the windows of which opens39.E-mail is a convenient, highly informal medium for conveying message among people __________well satisfies human needs.A.what B,who C.that D.for which40.According to a report recently released by the US National Research Council,the amount of space junk flowing in Earth’s orbit has reached a critical lever_________future space mission may become too dangerous to fly.A.thatB.whereC.whose D of which41.Marco Polo,who was a great Italian traveler, traveled all the way to China,_________was then called Cathy.A.whereB.whichC.whenD.what42.He arrived in New York in 1986,____________some time later, he became a writer.A.whenB.whereC.thatD.which43.It was almost midnight_________the ceremony was over.A.thatB.sinceC.when D,till44.Jenny smiled________her mother did when she was Jenny’s age.A.whatB.whereC.thatD.which45._________did you use to do________you don’t do now?A.46._______glitters is not gold not all those__________wander are lost.A.What,whoB.All that,whoC.All,thatD.What,that47.Sparking Lake in Jiuzhaigou is so beautiful a place_________people can memorize forever even it no longer exists in real life.A.thatB.whichC.asD.what48.I sent invitation to 100people to the party,__________turned up.A.of whom only a thirdB.only 30 of theseC.almost all of themD.and none of them49.There is no difficulty___________we can overcome.A.whichB.thatC.whatD.but50.Could you lend me a knife________A.which to open the canB.with which to open a canC.with which I opened the canD.with which I can use to open a canVocabularyComplete the following passage by using the words in the box.Each word can only be used once. Note that there is one word more than you need.Prederic Mishikn, who’s been a professor at Columbia Business School for almost 30 years, is good at solving problems and expressing ideas. Whether he’s sending in front of a lecture hall or engaged in a ____51______ conversion, his hands are always waving and pointing. When he was in_____52_______school,one of his professors was so annoyed bythis____53_____gesturing that he made the young economist sit on his hands whenever he visited the professor’s office.It t urns out, however, that Mishikn’s professor had it exactly wrong. Gesture doesn’t prevent but ____54_____clear thought and speech.Research______55____that the movements we make with our hands when wetalk_______56_____a kind of second language, adding information that is____57_______from our words. It is learning’s_____58_______code;Gestures reveals what we know. It also reveals what we don’t know. What’s more, the agreement(or______59_______of agreement)between what our voices say and how our hands move offers a ___60________to our readiness to learn.III. Reading ComprehensionSection ADirections:For each blank in the following passage there are four wordsorphrasesmarked A,B,C and D. Fill in each blank with the word or phrase that best fits thecontext.One of the big excuses for not learning languages in Britain is that when you try them out abroad, the person you are speaking to responds in__61__ English, making you feel about two feet tall—or should that be 36 cm?English people are known for their reluctance to accept changes leading to closer union with us European partners. __62__ according to organizations promoting English business, ____63_____language learning is concerned, that simply doesn’t __53__ in that 21st century.Trade Section UK aims to help British companies trading overseas. Its chief executive, Sir David Wright, says: “Language __64__ are good for business, good for jobs and help people in their career. Although many people may speak English __65__, they will usually negotiate in their own language. If we are to compete on an equal basis, it’s decisive that business ______66____ the challenge and uses languages more effectively.”The Council of Europe __67__ language learning as an important tool to improve communication and mutual understanding between individuals. The Center for Information on Language Teaching says that being able to speak __68__ language is a “basic life skill” and that the “language deficit in the UK has become an urgent economic, __69__ and political question.”The department for Education and Skills wants to __70__ teaching of modern foreign languages (MFT) at an earlier stage in the future. Primary school children will get greater __71__to foreign language learning. Currently, about 20 percent of primary schools offer MFL teaching. The Department wants to increase this __72__ by 2012 every child has an entitlement to study a language at primary school.Education and Skills secretary Estelle Morris is very __73__ about more primary schools taking up the __74__ challenge. Children are just so much more responsive___75_____an earlier age.61. A. broken B. perfect C. natural D. simple62. A. And B. But C. So D. Besides63. A. whose B. where C. which D. that64. A. technology B. Learners C. skills D. teachers65. A. at home B. in school C aboard D. Overseas66. A. takes up B. takes off C. takes over D. takes in67. A. finds B. thinks C. regards D. believes68. A. native B. local C. another D. certain69. A. physical B. mental C. spiritual D. social70. A. permit B. encourage C. demand D. challenge71. A. admission B. access C. chance D. approach72. A. in that B. that C. now that D. so that73. A. worried B. concerned C. positive D. negative74. A. language B. business C. competition D. learning75. A. to B. on C. at D. ofReading comprehension(A)I made a pledge (发誓) to myself on the way down to the vacation beach cottage. For two weeks I would try to be a loving husband and father. Totally loving. No ifs, ands or buts.The idea had come to me as I listened to a talk on my car radio. The speaker was quoting a Biblical (圣经的) passage about husbands being thoughtful of their wives. Then he went on to say, "Love is an act ofwill.A person can choose to love." To myself, I had to admit that I had been a selfish husband. Well, for two weeks that would change.And it did. Right from the moment I kissed Evelyn at the door and said, "That new yellow sweater looks great on you."Oh, Tom, you noticed," she said, surprised and pleased, maybe a little puzzled.After the long drive, I wanted to sit and read. Evelyn suggested a walk on the beach. I started to refuse, but then I thought, "Evelyn's been alone here with the kids all the week and now she wants to stay with me." We walked on the beach while the children flew their kites.So it went. Two weeks of not calling the Wall Street firm where I am a director; a visit to the shell museum though I usually hate museums. Relaxed and happy, that's how the whole vacation passed. I made a new pledge to keep on remembering to choose love.There was one thing that went wrong with my experiment, however. Evelyn and I still laugh about it today.Last night at our cottage, preparing for bed, Evelyn stared at me with the saddest expression." What's the matter" I asked her."Tom," she said in a voice filled with distress, "do you know something I don't""What do you mean"" Well...that checkup (体检) I had several weeks ago...our doctor (i)he tell you something about meTom, you've been so good to me...am I dying"It took a moment for it all to sink in. Then I burst out laughing."No, honey," I said, wrapping her in my arms. "You're not dying; I'm just starting to live."76. In the first paragraph, "No ifs, ands or buts" probably means ____.A. UnnecessarilyB. unconditionallyC. impossiblyD. unexpectedly77. During the two weeks on the beach, Tom showed more love to his wife because _____.A. she looked lovely in her new clothesB. she was seriously illC. he was determined to be a good husbandD. he had made a lot of money in Wall Street78.By saying "I'm just starting to live", Tom means that _____.A. he is beginning to feel regretful for what he did to his wifeB. he lived an unhappy life before and is now starting to changeC. he is just beginning to understand the real meaning of lifeD. he is just beginning to enjoy his life as a loving husband(B)As I was thinking about language learning the other day, the image of baking bread came into my mind．I compared some of the exercises and drills that we put ourselves through in order to learn a language to the various ingredients (原料) that go into baking a loaf of fresh bread．Real language learning takes place in human relationships．No one sits down and eats a cup of flour, even if he is hungry and in a hurry．You don' t become bilingual (双语的) by learning lists of vocabulary．You don' tbecome a speaker of a language by memorizing grammatical rules．You become bilingual by entering a community that uses that other language as its basic means of communication．I am not suggesting that we can make bread without ingredients．Flour is necessary, as are yeast (酵母), salt, water and other ingredients．Vocabulary is part of any language and will have to be learned．Grammatical rules exist in every language and cannot be ignored．But merely combining the appropriate ingredients in the recommended proportions does not result in bread．At best, you only end up with a ball of dough (面团)．In order to get bread, you have to apply heat to the dough．And in language learning, that heat comes from the community．Anyone who has learned a second language has experienced that heat．It creeps up your neck when you ask the babysitter “Have you already been eaten” when you meant to say, ‘‘Have you already eaten” When you try to say something quite innocent and the whole room bursts into laughter, you are experiencing the heat that turns raw dough into good bread．Remember the old saying, “If you can' t stand the heat, get out of the kitchen"．This is where language learning often breaks down because we find the heat uncomfortable and we stop the baking process．In other words, we can' t stand the heat, so we get out of the kitchen．However, the language learner who stays in the kitchen－in the heat－until the combined ingredients are thoroughly transformed will enjoy the richness of a quality loaf of bread. He is glad that he did not "get out of the kitchen” at the important moment when the oven seemed too hot.The dedicated language learner knows that becoming bilingual cannot be achieved without the heat.79.According to the author, you can possibly become a speaker of a language by ________．A．bearing millions of words and expressions in your mindB．using the language to communicate with those around youC．Knowing verb conjugations and grammatical rulesD．saying something innocent to be laughed at by others80.'What’s the purpose of illustration of the example-you ask the babysitter,"Have you already been eaten"When you meant to say,"Have you already eaten"A. To verify that you are sure to make some mistakes when you enter a community.B.To show that you should combine the ingredients in the recommended proportions.C. To prove that you may experience"heat"from the community in language learning.D. To indicate that being bilingual calls for your courage, confidence and perseverance.81.According to the passage, which of the following is NOT the necessity of baking bread and learning language?A．Excellent Skills．B．Various ingredients．C．Appropriate proportions．D．Uncomfortable heat．(C)Like most people, I’ve long understood that I’ll be judged by my occupation, that my profession is used by people to see how talented I am. Recently, however, I was disappointed to see that it also decides how I’m treated as a person.Last year I left a professional position as a small-town reporter and took a job waiting tables. As someone paid to serve food to people, I had customers say and do things to me I suppose they’d never say or do to the people they know. One night a man talking on his cell phone waved me away,then called me back with his finger a minute later, saying angrily that he was ready to order and asking where I’d been.I had waited tables during summers in college and was treated like a peon（勤杂工） by plenty of people. But at 19 years old, I believed I deserved inferior（低等的）treatment from professional adults. Besides, people responded to me differently after I told them I was in college. Customers would joke that one day I’d be sitting at their table, waiting to be served.Once I graduated I took a job at a community newspaper. From my first day, I heard a respectful tone from everyone who called me. I assumed this was the way the professional world worked--- politely and formally.I soon found out differently. I sat several feet away from a person in advertising department with a similar name. Our calls would often get mixed up and someone asking for Kristen would be transferred to Christie. The mistake was immediately clear. Perhaps it was because of money, but people used a tone with Kristen that they never used with me.My job title made people treat me with courtesy. So it was a shock to return to be the restaurant industry.It’s no secret that there’s a lot to put up with when waiting tables, and fortunately, much of it can be easily forgotten when you pocket the tips. The service industry exists to meet others’ needs. Still, it seemed that many of my customers didn’t get the difference between server and servant.I’m now applying to graduate school, which means someday I’ll return to a profession where people need to be nice to me in order to get what they want. I think I’ll take them to dinner first, and see how they treat someone whose job is to serve them.82.The author was disappointed to find that_____________83.A. one’s position is used to measure one’s intelligence.B. Talented people like her should fail to get a respectable jobC. one’s occupation affects the way one is treated as a person.D. professionals tend to look down upon manual workers.83. What does the author intend to say by the example in Paragraph 2A. Waiting tables is a hard job.B. Some customers are difficult to deal with.C. The man making a phone call is absent-minded.D. Some customers show no respect to those who serve them.84.What does the author imply by saying"... Many of my customers didn’t get the difference between server and servant (Lines 3-4, Para. 7)A. Those who cater to others' needs are destined to be looked down upon.B. Those working in the service industry shouldn't be heated as servants.C. Those serving others have to put up with rough treatment to earn a living.D. The majority of customers tend to look on a servant as 4. server nowadays.85. The author says one day she’ll take her customers to dinner in order to _______.A. see what kind of person they areB. experience the feeling of being servedC. shoe her generosity towards people inferior to herD.arouse their sympathy for people living a humble life(D)In 1784, five years before he became president of the United States, George Washington, 52, was nearly toothless. So he hired a dentist to transplant nine teeth into his jaw—having extracted them from the mouths of his slaves.That's a far different image from the cherry-tree-chopping George most people remember from their history books. But recently, many historianshave begun to focus on the roles slavery played in the lives of thefounding generation. They have been spurred in part by DNA evidence made available in 1998, which almost certainly proved Thomas Jefferson had fathered at least one child with his slave Sally Hemings. And only over the past 30 years have scholars examined history from the bottom up. Works of several historians reveal the moral compromises made by the nation's early leaders and the fragile nature of the country's infancy. More significantly, they argue that many of the Founding Fathers knew slavery was wrong—andyet most did little to fight it.More than anything, the historians say, the founders were hampered bythe culture of their time. While Washington and Jefferson privately expressed distaste for slavery, they also understood that it was part ofthe political and economic bedrock of the country they helped to create.For one thing, the South could not afford to part with its slaves. Owning slaves was "like having a large bank account," says Wiencek, authorof An Imperfect God: George Washington, His Slaves, and the Creation of America. 'The southern states would not have signed the Constitutionwithout protections for the "peculiar institution," including a clause that counted a slave as three fifths of a man for purposes of congressional representation.And the statesmen's political lives depended on slavery. The three-fifths formula handed Jefferson his narrow victory in the presidential election of 1800 by inflating the votes of the southern states in the Electoral College. Once in office, Jefferson extended slavery with the Louisiana Purchase in 1803; the new land was carved into 13 states,including three slave states.Still, Jefferson freed Hemings' children—though not Hemings herself or his approximately 150 other slaves. Washington, who had begun to believethat all men were created equal after observing the bravery of the black soldiers during the Revolutionary War, overcame the strong opposition of his relatives to grant his slaves their freedom in his will. Only a decade earlier, such an act would have required legislative approval in Virginia.86. In Paragraph 1,George Washington's dental surgery is mentionedto__________A．show the poor medical practice in the past.B．demonstrate the great cruelty of slavery in his days.C．stress the important role of slaves in the entire U.S. history. D．reveal an unknown aspect of his life and introduce the topic87.We may infer from the second paragraph that_____________.A. DNA technology has been widely applied to history research.B. In its early day. s the U. S. was confronted with delicate situations.C. historians deliberately made up some stories of Jefferson's life.D.Political compromises are easily found throughout the U. S. history.88. What do we learn about Thomas Jefferson?A. His political view changed his attitude towards slavery.B. His status as a father made him free the child slaves.C. His attitude towards slavery was complex.D. His affair with a slave ruined his reputation.89.Which of the following is TRUE according to the text?A. Some founding fathers benefited politically from slavery.B. Slaves in the old days did not have the right to vote.C. Slave owners usually had large savings accounts.D. Washington decided to free slaves due to moral considerations. Translation1.社会上，年轻人赶时髦，穿时尚衣服是常有的事。

上海市上海中学2016-2017学年高一上学期数学周练14Word版含答案

上海中学高一周练数学卷2016.12.22一. 填空题1.函数()f x =(0)x ≤的反函数是1()fx -= 2. 若4log 124x =，则x = 3. 函数2()lg(23)f x x x =--的递减区间是4. 函数21()12f x x =+(2)x <-的反函数是1()f x -= 5. 若函数6,2()3log ,2a x x f x x x -+≤⎧=⎨+>⎩(0a >且1)a ≠的值域是[4,)+∞，则实数a 的取值范围是 6. 若函数()8x f x =的图像经过点1(,)3a ，则1(2)f a -+=7. 若函数24,3()(1)1,3x x f x a x x ⎧-≥=⎨-+<⎩存在反函数，则实数a 的取值范围为8. 如果log 41a b =-，则a b +的最小值为9. 若实数t 满足()f t t =-，则称t 是函数()f x 的一个次不动点，设函数()ln f x x =与反函数的所有次不动点之和为m ，则m =10. 设lg lg lg 111()121418x x x f x =+++++，则1()()f x f x+= 11. 设方程24x x +=的根为m ，方程2log 4x x +=的根为n ，则m n +=12. 对区间I 上有定义的函数()g x ，记(){|(),}g I y y g x x I ==∈，已知定义域为[0,3]的函数()y f x =有反函数1()y f x -=，且1([0,1))[1,2)f -=，1((2,4])[0,1)f -=，若方程 ()0f x x -=有解0x ，则0x =二. 选择题13. 如果23499log 3log 4log 5log 100x =⋅⋅⋅⋅⋅⋅⋅，则x ∈（）A. (1,2)B. (2,3)C. (5,6)D. (6,7)14. 函数2x xe e y --=的反函数是（）A. 奇函数，在(0,)+∞上是减函数B. 偶函数，在(0,)+∞上是减函数C. 奇函数，在(0,)+∞上是增函数D. 偶函数，在(0,)+∞上是增函数15. 已知函数()f x 为R 上的单调函数，1()f x -是它的反函数，点(1,3)A -和点(1,1)B 均在函数()f x 的图像上，则不等式1|(2)|1x f -<的解集为（）A. (1,1)-B. (1,3)C. 2(0,log 3)D.2(1,log 3)16. 设,,0x y z >，且12xyz y z ++=，则422log log log x y z ++的最大值为（）A. 3B. 4C. 5D. 6三. 解答题17. 已知910390x x -⨯+≤，求函数111()4()242x x y -=-+的最大值和最小值；18. 给定实数a ，0a ≠且1a ≠，设函数11x y ax -=-；（1）求证：经过这个函数图像上的任意两个不同的点的直线不平行于x 轴；（2）判断此函数的图像是否关于直线y x =对称，说明你的理由；19. 作出下列函数的大致图像；（1）3|log |||y x =；（2）12log (24)y x =+；20. 设a 是实数，函数()4|2|x xf x a =+-；（1）求证： ()f x 不是奇函数；（2）当0a >时，求()f x 的值域；21. 设函数()n n f x x bx c =++，*n N ∈，b 、c R ∈；（1）设2n ≥，1b =，1c =-，证明：()n f x 在区间1(,1)2内存在唯一的零点；（2）设2n =，若对任意12,[1,1]x x ∈-，有2122|()()|4f x f x -≤，求b 的取值范围；参考答案一. 填空题1. 2x -(0)x ≤2.116 3. (,1)-∞- 4. (3)x > 5. (1,2] 6. 237. (1,2] 8. 1 9. 0 10. 3 11. 4 12. 2二. 选择题13. D 14. C 15. C 16. A三. 解答题17. max ()(0)2f x f ==，min ()(1)1f x f ==；18.（1）略；（2）1()()f x f x -=，是； 19. 略；20.（1）略；（2）当102a <<，值域为2[,)a +∞；当12a ≥，值域为1[,)4a -+∞； 21.（1）单调递增，1()02n f <，(1)0n f >；（2）[2,2]-；。

2016-2017学年上海中学高一(上)期末数学试卷(解析版)

2016-2017学年上海中学高一（上）期末数学试卷一.填空题1．（3.00分）函数f（x）=+lg（3x+1）的定义域是．2．（3.00分）函数f（x）=x2（x≥1）的反函数f﹣1（x）=．3．（3.00分）若幂函数f（x）的图象经过点，则该函数解析式为f（x）=．4．（3.00分）若对任意不等于1的正数a，函数f（x）=a x+2﹣3的图象都过点P，则点P的坐标是．5．（3.00分）已知f（x）=ax2+bx是定义在[a﹣3，2a]上的偶函数，那么a=，b=．6．（3.00分）方程log2（x+1）2+log4（x+1）=5的解是．7．（3.00分）已知符号函数sgn（x）=，则函数y=sgn（|x|）+|sgn（x）|的值域为．8．（3.00分）已知f（x）是定义在R上的奇函数，当x＜0时，f（x）=x2+x，则函数f（x）的解析式为f（x）=．9．（3.00分）函数的单调增区间为．10．（3.00分）设函数y=f（x）存在反函数f﹣1（x），若满足f（x）=f﹣1（x）恒成立，则称f（x）为“自反函数”，如函数f（x）=x，g（x）=b﹣x，（k≠0）等都是“自反函数”，试写出一个不同于上述例子的“自反函数”y=．11．（3.00分）方程x2+2x﹣1=0的解可视为函数y=x+2的图象与函数的图象交点的横坐标，若方程x4+ax﹣4=0的各个实根x1，x2，…，x k（k≤4）所对应的点（i=1，2，…，k）均在直线y=x的同侧，则实数a的取值范围是．12．（3.00分）对于函数y=f（x），若存在定义域D内某个区间[a，b]，使得y=f （x）在[a，b]上的值域也是[a，b]，则称函数y=f（x）在定义域D上封闭．如果函数（k≠0）在R上封闭，那么实数k的取值范围是．二.选择题13．（3.00分）已知f（x）=ax3+bx+1（ab≠0），若f（2013）=k，则f（﹣2013）=（）A．k B．﹣k C．1﹣k D．2﹣k14．（3.00分）定义在R上的函数f（x）在区间（﹣∞，2）上是增函数，且f（x+2）的图象关于x=1对称，则（）A．f（1）＜f（5）B．f（1）＞f（5）C．f（1）=f（5）D．f（0）=f（5）15．（3.00分）汽车的“燃油效率”是指汽车每消耗1升汽油行驶的里程，如图描述了甲、乙、丙三辆汽车在不同速度下燃油效率情况，下列叙述中正确的是（）A．消耗1升汽油，乙车最多可行驶5千米B．以相同速度行驶相同路程，三辆车中，甲车消耗汽油最多C．某城市机动车最高限速80千米/小时，相同条件下，在该市用丙车比用乙车更省油D．甲车以80千米/小时的速度行驶1小时，消耗10升汽油16．（3.00分）设函数若关于x的方程f（x）=a有四个不同的解x1，x2，x3，x4，且x1＜x2＜x3＜x4，则x3（x1+x2）+的取值范围是（）A．（﹣3，+∞）B．（﹣∞，3）C．[﹣3，3）D．（﹣3，3]三.解答题17．在平面直角坐标系中，作出下列函数的图象；（1）；（2）．18．已知集合D={x|32x﹣10•3x+2+36≤0，x∈R}，求函数（x ∈D）的值域．19．设函数f（x）=k•a x﹣a﹣x（a＞0且a≠1）是奇函数．（1）求常数k的值；（2）若，且函数g（x）=a2x﹣a﹣2x﹣2mf（x）在区间[1，+∞）上的最小值为﹣2，求实数m的值．20．已知函数；（1）当m=2时，判断f（x）在（﹣∞，0）上的单调性并证明；（2）若对任意x∈R，不等式f（2x）＞0恒成立，求m的取值范围；（3）讨论函数y=f（x）的零点个数．21．已知a∈R，函数f（x）=log2[（a﹣3）x+3a﹣4]；（1）当a=2时，解不等式；（2）若函数y=f（x2﹣4x）的值域为R，求a的取值范围；（3）若关于x的方程解集中恰好只有一个元素，求a的取值范围．2016-2017学年上海中学高一（上）期末数学试卷参考答案与试题解析一.填空题1．（3.00分）函数f（x）=+lg（3x+1）的定义域是（﹣，1）．【分析】由分母中根式内部的代数式大于0，对数式的真数大于0联立不等式组求解x的取值集合得答案．【解答】解：由，解得：﹣．∴函数f（x）=+lg（3x+1）的定义域是（﹣，1）．故答案为：（﹣，1）．2．（3.00分）函数f（x）=x2（x≥1）的反函数f﹣1（x）=（x≥1）．【分析】由y=x2（x≥1），解得x=（y≥1），把x与y互换即可得出．【解答】解：由y=x2（x≥1），解得x=（y≥1），把x与y互换可得：y=，∴f（x）=x2（x≥1）的反函数f﹣1（x）=（x≥1）．故答案为：（x≥1）．3．（3.00分）若幂函数f（x）的图象经过点，则该函数解析式为f（x）=．【分析】设出幂函数的解析式，把点的坐标代入解析式求解即可．【解答】解：设幂函数f（x）=x a，其图象经过点，∴27a=，解得a=﹣；∴函数f（x）=．故答案为：．4．（3.00分）若对任意不等于1的正数a，函数f（x）=a x+2﹣3的图象都过点P，则点P的坐标是（﹣2，﹣2）．【分析】指数函数恒过定点（0，1），据此令指数型函数的指数为0即可求得最终结果．【解答】解：指数函数恒过定点（0，1），据此可令x+2=0，解得：x=﹣2，f（﹣2）=a﹣2+2﹣3=﹣2，即函数f（x）=a x+2﹣3 恒过定点（﹣2，﹣2）．故答案为：（﹣2，﹣2）．5．（3.00分）已知f（x）=ax2+bx是定义在[a﹣3，2a]上的偶函数，那么a=1，b=0．【分析】依照偶函数的定义，对定义域内的任意实数，f（﹣x）=f（x），且定义域关于原点对称，a﹣3=﹣2a．【解答】解：∵f（x）=ax2+bx是定义在[a﹣3，2a]上的偶函数，∴f（﹣x）=f（x），∴b=0，又a﹣3=﹣2a，∴a=1，故答案1，0．6．（3.00分）方程log2（x+1）2+log4（x+1）=5的解是3．【分析】由对数的换底公式和运算法则，把原式转化为log4（x+1）5=5，由此能求出x的值．【解答】解：∵log2（x+1）2+log4（x+1）=5，∴log4（x+1）4+log4（x+1）=5，∴log4（x+1）5=5，∴（x+1）5=45，∴x=3．故答案为：3．7．（3.00分）已知符号函数sgn（x）=，则函数y=sgn（|x|）+|sgn（x）|的值域为{0，2} ．【分析】结合函数的解析式分类讨论x＞0，x=0，x＜0三种情况即可求得函数的值域．【解答】解：分类讨论：当x＞0时：y=sgn（|x|）+|sgn（x）|=sgn（x）+1=1+1=2；当x=0时：y=sgn（|x|）+|sgn（x）|=sgn（x）+0=0+0=0；当x＞0时：y=sgn（|x|）+|sgn（x）|=sgn（x）+1=﹣1+1=0；综上可得：函数y=sgn（|x|）+|sgn（x）|的值域为{0，2}．故答案为：{0，2}．8．（3.00分）已知f（x）是定义在R上的奇函数，当x＜0时，f（x）=x2+x，则函数f（x）的解析式为f（x）=．【分析】首先利用奇函数的性质可得f（0）=0，然后结合奇函数的性质求解x＞0时函数的解析式，最后将函数的解析式写出分段函数的形式即可．【解答】解：由奇函数的性质可得：f（0）=0，设x＞0，则﹣x＜0，此时有：﹣f（x）=f（﹣x）（﹣x）2+（﹣x）=x2﹣x，则f（x）=﹣x2+x，且当x=0时，﹣x2+x=0，综上可得：函数的解析式为：．9．（3.00分）函数的单调增区间为（﹣∞，1]和[3，5]．．【分析】首先将解析式中的指数看作一个函数讨论其单调性，然后利用复合函数同增异减的原则讨论原函数的单调性即可．【解答】解：绘制函数y=|x2﹣6x+5|的图象如图所示：观察函数图象可得函数的单调递增区间为：[1，3]和[5，+∞）单调递减区间为：（﹣∞，1]和[3，5]指数函数y=0.3x在定义域内单调递减，结合复合函数同增异减的原则可得函数的单调递增区间，即函数y=|x2﹣6x+5|的单调递减区间：（﹣∞，1]和[3，5]．故答案为：（﹣∞，1]和[3，5]．10．（3.00分）设函数y=f（x）存在反函数f﹣1（x），若满足f（x）=f﹣1（x）恒成立，则称f（x）为“自反函数”，如函数f（x）=x，g（x）=b﹣x，（k≠0）等都是“自反函数”，试写出一个不同于上述例子的“自反函数”y=（0≤x ≤1）．【分析】根据题意，只要写出满足条件的函数即可，如y=（0≤x≤1）等．【解答】解：根据题意，设函数y=，（0≤x≤1），则y2=1﹣x2，∴x2=1﹣y2，∴x=（0≤y≤1），交换x、y得反函数y=（0≤x≤1），满足题意．故答案为：（0≤x≤1）．11．（3.00分）方程x2+2x﹣1=0的解可视为函数y=x+2的图象与函数的图象交点的横坐标，若方程x4+ax﹣4=0的各个实根x1，x2，…，x k（k≤4）所对应的点（i=1，2，…，k）均在直线y=x的同侧，则实数a的取值范围是（﹣∞，﹣6）∪（6，+∞）．【分析】原方程等价于x3+a=，分别作出y=x3+a与y=的图象：分a＞0与a＜0讨论，利用数形结合即可得到结论．【解答】解：方程的根显然x≠0，原方程x4+ax﹣4=0，等价为方程x3+a=，原方程的实根是曲线y=x3+a与曲线y=的交点的横坐标；曲线y=x3+a是由曲线y=x3向上或向下平移|a|个单位而得到的．若交点（x i，）（i=1，2，k）均在直线y=x的同侧，因直线y=x与y=交点为：（﹣2，﹣2），（2，2）；所以结合图象可得：或，解得a＞6或a＜﹣6，即实数a的取值范围是（﹣∞，﹣6）∪（6，∞），故答案为：（﹣∞，﹣6）∪（6，+∞）．12．（3.00分）对于函数y=f（x），若存在定义域D内某个区间[a，b]，使得y=f （x）在[a，b]上的值域也是[a，b]，则称函数y=f（x）在定义域D上封闭．如果函数（k≠0）在R上封闭，那么实数k的取值范围是（1，+∞）．【分析】由题意便知方程组至少有两个解，从而可得到至少有两个解，从而有k=1+|x|＞1，这样即求出k的取值范围．【解答】解：根据题意知方程至少有两个不同实数根；即至少有两个实数根；∴；∴k=1+|x|＞1；∴实数k的取值范围为（1，+∞）．故答案为：（1，+∞）．二.选择题13．（3.00分）已知f（x）=ax3+bx+1（ab≠0），若f（2013）=k，则f（﹣2013）=（）A．k B．﹣k C．1﹣k D．2﹣k【分析】将f（x）=ax3+bx+1转化为f（x）﹣1=ax3+bx，则函数F（x）=f（x）﹣1为奇函数，然后利用奇函数的性质进行求解．【解答】解：∵f（x）=ax3+bx+1，∴f（x）﹣1=ax3+bx，令F（x）=f（x）﹣1=ax3+bx，∵ab≠0，∴函数F（x）=f（x）﹣1=ax3+bx是奇函数，∴F（﹣2013）=﹣F（2013），即f（﹣2013）﹣1=﹣[f（2013）﹣1]=﹣k+1，∴f（﹣2013）=2﹣k．故选：D．14．（3.00分）定义在R上的函数f（x）在区间（﹣∞，2）上是增函数，且f（x+2）的图象关于x=1对称，则（）A．f（1）＜f（5）B．f（1）＞f（5）C．f（1）=f（5）D．f（0）=f（5）【分析】由f（x+2）的图象关于x=1对称，得f（x+2）=f（2﹣x+2）=f（4﹣x），令x=﹣1可得答案．【解答】解：因为f（x+2）的图象关于x=1对称，所以f（x+2）=f（2﹣x+2）=f （4﹣x），所以f（﹣1+2）=f[（4﹣（﹣1）]，即f（1）=f（5），故选：C．15．（3.00分）汽车的“燃油效率”是指汽车每消耗1升汽油行驶的里程，如图描述了甲、乙、丙三辆汽车在不同速度下燃油效率情况，下列叙述中正确的是（）A．消耗1升汽油，乙车最多可行驶5千米B．以相同速度行驶相同路程，三辆车中，甲车消耗汽油最多C．某城市机动车最高限速80千米/小时，相同条件下，在该市用丙车比用乙车更省油D．甲车以80千米/小时的速度行驶1小时，消耗10升汽油【分析】根据函数图象的意义逐项分析各说法是否正确．【解答】解：对于A，由图象可知当速度大于40km/h时，乙车的燃油效率大于5km/L，∴当速度大于40km/h时，消耗1升汽油，乙车的行驶距离大于5km，故A错误；对于B，由图象可知当速度相同时，甲车的燃油效率最高，即当速度相同时，消耗1升汽油，甲车的行驶路程最远，∴以相同速度行驶相同路程，三辆车中，甲车消耗汽油最少，故B错误；对于C，由图象可知当速度小于80km/h时，丙车的燃油效率大于乙车的燃油效率，∴用丙车比用乙车更省油，故C正确；对于D，由图象可知当速度为80km/h时，甲车的燃油效率为10km/L，即甲车行驶10km时，耗油1升，故行驶1小时，路程为80km，燃油为8升，故D错误．故选：C．16．（3.00分）设函数若关于x的方程f（x）=a有四个不同的解x1，x2，x3，x4，且x1＜x2＜x3＜x4，则x3（x1+x2）+的取值范围是（）A．（﹣3，+∞）B．（﹣∞，3）C．[﹣3，3）D．（﹣3，3]【分析】作函数的图象，从而可得x1+x2=﹣4，x3x4=1，≤x3＜1，从而解得．【解答】解：作函数的图象如下，，结合图象，A，B，C，D的横坐标分别为x1，x2，x3，x4，故x1+x2=﹣4，x3x4=1，故=﹣4x3，∵0＜﹣log2x3≤2，∴≤x3＜1，∴﹣3＜﹣4x3≤3，故选：D．三.解答题17．在平面直角坐标系中，作出下列函数的图象；（1）；（2）．【分析】根据指数函数的图象和性质即可画出图象．【解答】解：（1）函数；的图形如图：（2）．函数是偶函数，是x＞0时，y=图象关于y轴对称后，向下平移1个单位得到的图象，如图所示，18．已知集合D={x|32x﹣10•3x+2+36≤0，x∈R}，求函数（x ∈D）的值域．【分析】由题意求解不等式首先确定集合D，然后整理函数的解析式，最后利用二次函数在给的区间上求值域的方法求解函数的值域即可．【解答】解：集合D中不等式即：（3x）2﹣90×3x+729≤0，则：（3x﹣9）（3x﹣81）≤0，9≤3x≤81，解得2≤x≤4，∴1≤log2x≤2．所需求解值域的函数解析式为：f（x）=（log2x﹣1）（log2x﹣2），结合二次函数的性质可得：当log2x=1 或log2x=2 时，函数取得最大值0；当时，函数取得最小值；函数的值域为．19．设函数f（x）=k•a x﹣a﹣x（a＞0且a≠1）是奇函数．（1）求常数k的值；（2）若，且函数g（x）=a2x﹣a﹣2x﹣2mf（x）在区间[1，+∞）上的最小值为﹣2，求实数m的值．【分析】（1）方法一、由奇函数的性质：f（0）=0，解方程可得k=1，检验成立；方法二、运用奇函数的定义，由恒等式的性质即可得到k=1；（2）求得a=3，即有g（x）=32x﹣3﹣2x﹣2m（3x﹣3﹣x），令t=3x﹣3﹣x，则t是关于x的增函数，可得，h（t）=t2﹣2mt+2=（t﹣m）2+2﹣m2，讨论对称轴和区间的关系，运用单调性，可得最小值，解方程可得m的值．【解答】（1）解法一：函数f（x）=k•a x﹣a﹣x的定义域为R，f（x）是奇函数，所以f（0）=k﹣1=0，即有k=1．当k=1时，f（x）=a x﹣a﹣x，f（﹣x）=a﹣x﹣a x=﹣f（x），则f（x）是奇函数，故所求k的值为1；解法二：函数f（x）=k•a x﹣a﹣x的定义域为R，由题意，对任意x∈R，f（﹣x）=﹣f（x），即k•a﹣x﹣a x=a﹣x﹣k•a x，（k﹣1）（a x+a﹣x）=0，因为a x+a﹣x＞0，所以，k=1．（2）由，得，解得a=3或（舍）．所以g（x）=32x﹣3﹣2x﹣2m（3x﹣3﹣x），令t=3x﹣3﹣x，则t是关于x的增函数，，g（x）=h（t）=t2﹣2mt+2=（t﹣m）2+2﹣m2，当时，则当时，，解得；当时，则当t=m时，，m=±2（舍去）．综上，．20．已知函数；（1）当m=2时，判断f（x）在（﹣∞，0）上的单调性并证明；（2）若对任意x∈R，不等式f（2x）＞0恒成立，求m的取值范围；（3）讨论函数y=f（x）的零点个数．【分析】（1）当m=2时，利用函数单调性的定义即可判断f（x）在（﹣∞，0）的单调性，并用定义证明．（2）利用参数分离法将不等式f（2x）＞0恒成立，进行转化，求m的取值范围；（3）根据函数的单调性和最值，即可得到结论．【解答】解：（1）当m=2，且x＜0时，f（x）=﹣x+﹣1是单调递减的．证明：设x1＜x2＜0，则f（x1）﹣f（x2）=﹣x1+﹣1﹣（﹣x2+﹣1）=（x2﹣x1）+（﹣）=（x2﹣x1）+=（x2﹣x1）（1+）又x1＜x2＜0，所以x2﹣x1＞0，x1x2＞0，所以（x2﹣x1）（1+）＞0所以f（x1）﹣f（x2）＞0，即f（x1）＞f（x2），故当m=2时，f（x）=﹣x+﹣1在（﹣∞，0）上单调递减的．（2）由f（2x）＞0得|2x|+﹣1＞0，变形为（2x）2﹣2x+m＞0，即m＞2x﹣（2x）2而2x﹣（2x）2=﹣（2x﹣）2+，当2x=即x=﹣1时（2x﹣（2x）2）max=，所以m＞．（3）由f（x）=0可得x|x|﹣x+m=0（x≠0），变为m=﹣x|x|+x（x≠0）令g（x）=x﹣x|x|=，作y=g（x）的图象及直线y=m，由图象可得：当m＞或m＜﹣时，f（x）有1个零点．当m=或m=0或m=﹣时，f（x）有2个零点；当0＜m＜或﹣＜m＜0时，f（x）有3个零点．21．已知a∈R，函数f（x）=log2[（a﹣3）x+3a﹣4]；（1）当a=2时，解不等式；（2）若函数y=f（x2﹣4x）的值域为R，求a的取值范围；（3）若关于x的方程解集中恰好只有一个元素，求a的取值范围．【分析】（1）利用题意得到对数不等式，求解不等式即可求得最终结果；（2）将原问题转化为二次函数的问题，结合二次函数的开口方向和判别式得到关于实数a的不等式组，求解不等式组即可；（3）将原问题转化为函数只有一个跟的问题，然后分类讨论即可求得最终结果．【解答】解：（1）当x=2时，f（x）=log2（﹣x+2），则不等式即：，据此可得：，即不等式的解集为．（2）函数，设函数y=（a﹣3）（x2﹣4x）+（3a﹣4）的值域为M，则（0，+∞）⊆M，当a﹣3=0，a=3时不满足题意，结合二次函数的性质可得：，即：，据此可得实数a的取值范围是{a|a≥8}．（3）满足题意时，恰好有一个解，即：，原问题：等价于方程，（a﹣3）2+（a﹣4）x﹣1=0（*）在满足只有唯一解方程（*）化为[（a﹣3）x﹣1]（x+1）=0①若a=3时，解x=﹣1，此时，满足题意；②若a=2时，两根均为x=﹣1，此时，也满足．③若a≠2且a≠3时，两根为，当时，；当x=﹣1时，依题意，（3a﹣3）（2a﹣1）＜0，解得综上，a的取值范围是。

2016-2017上海市上海中学2017届高三上学期周练英语试题( 3 )

上海中学高三英语周练分析Section A17. Luckily, the bullet narrowly missed the captain __________ an inch .A. byB.atC.toD. from18. Understanding the cultural habits of another nation, especially _______ containing as many different subcultures as the United States, is a complex task.A. oneB. the oneC. thatD. those19. The little boy walked in slowly lifting a stone______________.A. half of his weightB. half by his weightC. half his weightD. half weight of his20. The customers complained that not only ___________high, but he didn’t do a good repair job.A.he chargedB.was he chargedC.did he chargeD.he was charged21. The conference in Copenhagen _____ to bring the US and China into a global agreement, but produced nothing of substance.A. originally intendedB. intended originallyC. was originally intendedD. was originally intending22. A giant of a man was sitting next to the door, who, when he rose to greet me, _______ nearly seven feet tall.A. standingB. stoodC. was standingD. stands23. The government has listed a number of tourist attractions, including some____ significant sites.A. historicB. historicalC. historicallyD. historian24. The vast flood plain, known as the American bottom, stretches as far to the north and south as ____ can see.A. eyeB. an eyeC. the eyeD. one’s eyeSection B(A)Many a young person (25)_________(tell) me he wants to be a writer. I always encourage such people, (26)_________ I also explain tha t there’s a big difference between “being a writer” and writing. In most cases individuals are dreaming of wealth and fame, not the long hours alone at a typewriter. “You’ve got to want to write,” I say to them, not want to be a writer.”The reality is that writing is a lonely, private and poor-paying affair. For every writer kissed by fortune there are thousands more(27)_________ longing is never rewarded. When I left a 20-year career in the US Coast Guard to become a freelance writer(自由撰稿者), I had no prospects at all. What I did have was a friend who found me a room in (28)_________ apartment building in New York. It didn’t even matter that it was cold and had no bathroom. I immediately bought used manual typewriter and felt like a genuine writer.After a year or so, however, I still hadn’t got a break and began to doubt myself. It was so hard to sell a story(29)_________ I barely made enough to eat. But I knew I wanted to write. I had dreamed about it for years, I wasn’t going to be one of those pe ople who die wondering. What if? I would keep putting my dream to the test---(30)________ ________ it meant living with uncertainly and fear of failure. This is the shadowland of hope, and any one with a dream must learn to live there.(B)Every year dozens of films are released,yet(33)____________are forgotten after six months ?Movies come and go,as throwaway as popcorn bags left on the floor of a cinema.But of those fe w films that do stay in people‘s minds,there is one that is truly―evergreen‖.(34)______you‘re young or old,or wherever you are in the world,the1939classic Gone with the Wind never seems to become unpopular.December2015the film celebrated its75th birthday. The movie is based on a best-selling book of the same name by US author Margaret Mitchell.Holly wood was soon interested in turning the novel into a movie.The story(35)______in the periods before,during and after the American Civil War(1861-6 5),(35)______the war is more of a backdrop(背景)to the story than an important part of it.The story is about relations between members of high-class southern families.At the heart of the film is Scarlett O‘Hara.Beautiful and strong-willed,Scarlett is in lovewith a man,Ashley Wilkes,whose heart belongs to(36)______,Melanie Hamilton.Still,she triesto win Ashley‘s heart.One man,Rhett Butler,is especially interested in Scarlett.Rhett is as wild in his own way as she is.But although she flirts(调情)with Rhett,and despite the fact that she eventually marries him,she never really loves Rhett.It‘s only when she finally realizes that she can‘t have Ashley(37) ______she turns back to her husband.But,(38)______anyone who has seen the movie will know,by that point Rhett doesn‘t want her back and Scarlett is left with nobody(39)______(love).This Civil War period piece repaid the time and effort of the filmmakers who worked on it. Over two decades,it held the record for making the most money of any film ever(40)______ (make).It‘s the kind of movie that every studio dreams of making.Section CDirection: Complete following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.In the world of entertainment, TV talk shows have undoubtedly ___41_____ every inch of space on daytime television. And anyone who watches them ____42___ knows that each one varies in style and format. But no two shows are more profoundly opposite in ____43___, while at the same time standing out above the rest, than the Jerry Springer and the Oprah Winfrey shows.Jerry Springer could easily be considered the king of "trash talk". The topics on his show are as shocking as shocking can be. For example, the show takes the ever-common talk show themes of love, sex, cheating, guilt, hate, conflict and morality to a different level. ___44___, the Jerry Springer show is a display and __45____ of society's moral catastrophes, yet people are willing to eat up the intriguing predicaments (困境)of other people's lives.Like Jerry Springer, Oprah Winfrey takes TV talk show to its ___46___, but Oprah goes in the opposite direction. The show focuses on the improvement of society and an individual's quality of life. Topics range from teaching your children responsibility, managing 'your work week, to getting to know your neighbors.Compared to Oprah, the Jerry Springer show looks like poisonous waste being dumped on society. Jerry ends every show with a "final word". He makes a small speech that sums up the entire ___47___ of the show. Hopefully, this is the part where most people will learn something veryvaluable.___48___ as it is, the Oprah show is not for everyone. The show's main ___49__ audience are middle-class Americans. Most of these people have the time, money, and stability to deal with life's tougher problems. Jerry Springer, on the other hand, has more of an association with the young adults of society. These are 18 to 21-year-olds whose main troubles in life involve love, relationship, sex, money and peers. They are the ones who see some value and lessons to be learned underneath the show's exploitation.While the two shows are as different as night and day, both have ___50__ the talk show circuit for many years now. Each one caters to a different audience while both have a strong following from large groups of fans. Ironically, both could also be considered pioneers in the talk show world. III. Reading ComprehensionSection A CloseAs crime skyrockets in many communities, people are finally beginning to look for long-lasting, effective answers to stem the tide of juvenile crime. Reaching the youth who have committed a crime before they become 51 criminals is an essential step in 52 the crime trend. One possible solution may be the establishment of teen court.Unlike a trial court (初审法院), teen court is known as a 53 court for youths who have committed an offense. Teen courts primarily deal with 54 offenders. After arrest, the young offender must plead guilty to the 55 in teen court. With the teen court's permission, the offender agrees to be sentenced and abide by the decision of a peer jury (陪审团) of the same age. For example, a county teen court in Illinois gives young offenders a chance to 56 their arrests from their permanent record by performing community service or other 57 ordered by the court. 58 , as an essential component to the sentence, the offender must sit in on one or more future peer juries to 59 a sentence foe other offenders. It should be pointed out that a judge is present to 60 the proceedings of the court.The teen court 61 the strain on the regular court system and has been implemented in 426 communities since the first teen court opened in Odessa, Texas. 62 giving the offender a second chance, it gives the youth a chance to participate in the legal 63 .The 64 purpose of the teen court is to educate and motivate both the offenders and the teen volunteers while simultaneously promoting better communication between the accused, the 65 , the police and the legal system. By offering this alternative system, teen court allows those teens who have made a bad decision an opportunity to recognize their mistake and learn from it.51. A. suspicious B. hardened C. amateur D. famous52. A. reversing B. following C. reflecting D. starting53. A. civilian B. supreme C. sentencing D. lower54. A. violent B. convicted C. persistent D. first55. A. charge B. murder C. mercy D. defense56. A. prevent B. escape C. clear D. move57. A. jobs B. roles C. penalties D. duties58. A. However B. Therefore C. Moreover D. Instead59. A. announce B. determine C. serve D. receive60. A. overlook B. instruct C. oversee D. rule61. A. accelerates B. suffers C. increases D. eases62. A. Apart from B. In spite of C. Rather than D. Because of63. A. progress B. process C. access D. profession64. A. exclusive B. principal C. legal D. internal65. A. community B. county C. school D. court（A）It has been thought and said that Africans are born with musical talent. Because music is so important in the lives of many Africans and because so much music is performed in Africa, we are inclined to (倾向于……) think that all Africans are musicians. The impression is strengthened when we look at ourselves and find that we have become largely a society of musical spectators(旁观者). Music is important to us, but most of us can be considered consumers rather than producers of music. We have records, television, concerts, and radio to fulfill many of our musical needs. In most situations where music is performed in our culture it is not difficult to distinguish the audience from the performers, but such is often not the case in Africa. Alban Ayipaga, a Kasena semiprofessional musician from northern Ghana, says that when his flute (长笛) and drum ensemble (歌舞团) is performing. “Anybody can take part.”This is true, but Kasena musicians recognize that not all people are equally capable of taking part in the music. Some can sing along with the drummers, but relatively few can drum and even fewer can play the flute along with the ensemble. It is fairly common in Africa for there to be an ensemble of expert musicians surrounded by others who join in by clapping, singing, or somehow adding to the totality of music sound. Performances often take place in an open area (that is, not on a stage) and so the lines between the performing nucleus and the additional performers, active spectators, and passive spectators may be difficult to draw from our point of view.66. The difference between us and Africans, as far as music is concerned, is that________.A) most of us are consumers while most of them are producers of musicB) we are musical performers and they are semiprofessional musiciansC) most of us are passive spectators while they are active spectatorsD) we are the audience and they are the additional performers67. The word “such” (Line 6) refers to the fact that ________.A) music is performed with the participation of the audienceB) music is performed without the participation of the audienceC) people tend to distinguish the audience from the performersD) people have records, television sets and radio to fulfill their musical needs68. The author of the passage probably agrees that ________.A) all Africans are musical and therefore much music is performed in AfricaB) not all Africans are born with musical talent although music is important in their livesC) most Africans are capable of joining in the music by playing musical instrumentsD) most Africans perform as well as professional musicians69. The best title for this passage would be ________.A) The Importance of Music to African PeopleB) Differences Between African Music and Music of Other CountriesC) The Relationship Between Musicians and Their AudienceD) A Characteristic Feature of African Musical PerformancesBIs there a magic cutoff period when offspring become accountable for their own actions? Is there a wonderful moment when parents can become spectators (旁观者) in the lives of their children and shrug, "It' s their life," and feel nothing?When I was in my twenties, I stood in a hospital corridor waiting for doctors to put a few stitches in my son' s head. I was asked, "When do you stop worrying?" A nurse said, "When they get out of the accident stage." My mother just smiled faintly and said nothing.When I was in my thirties, I sat on a little chair in a classroom and heard how one of my children talked incessantly, disrupted (打断) the class, and was headed for a career making license plates. As if to read my mind, a teacher said, "Don't worry. They all go through this stage, and then you can sit back, relax, and enjoy them." My mother listened and said nothing.When I was in my forties, I spent a lifetime waiting for the phone to ring and the cars to come home, the front door to open.My friends said that when my kids got married I could stop worrying and lead my own life. I wanted to believe that, but I was haunted by my mother' s wan ( 淡淡的) smile and her occasional words, "You look pale. Are you all right? Call me the minute you get home."Can it be that parents are sentenced to a lifetime of worry? Is concern for one another handed down like a torch to blaze the trail of human frailties and the fears of the unknown? Is concern a curse? Or is it a virtue that elevates us to the highest form of life?One of my children became quite irritable recently, saying to me, "Where were you? I' ve been calling for three days, and no one answered. I was worried! ! !"I smiled a warm smile.70. The author intends to tell us in the passage that_________A. Parents long for a period when they no longer worry about their children.B. There is no time when parents have no worry about children.C. It’s parents’ duty to worry about their children.D. Parents don’t have to worry about their children.71. We can infer from the sentence “My mother just smiled faintly and said nothing.” that_________A.Her mother shared the same idea as the nurseB. Her mother wouldn’t express her opinion upon the matterC. Her mother felt relieved to know there was nothing serious about her grandsonD. Her mother didn’t agree with the nurse72. The author mentioned her ages of twenties, thirties, forties, and fifty in order to show_________A. the hard time she experiences in her life.B. the different stages of her childrenC. she had been worrying about her children in her life.D. the support she received from her mother.73.What can we infer from the sentence “ I smiled a warm smile” ?A. Finally the mother didn’t need to worry about the children.B. The mother was pleased that her child began to worry about her, too.C. At last, the mother could live her own life without worry.D. The mother felt satisfied that she had succeeded in turning her children into adults.COf all the changes that have taken place in English-language newspapers during the past quarter-century, perhaps the most far-reaching has been the inexorable decline in the scope and seriousness of their arts coverage.It is difficult to the point of impossibility for the average reader under the age of forty to imagine a time when high-quality arts criticism could be found in most big-city newspapers. Yet a considerable number of the most significant collections of criticism published in the 20th century consisted in large part of newspaper reviews. To read such books today is to marvel at the fact that their learned contents were once deemed suitable for publication in general-circulation dailies.We are even farther removed from the unfocused newspaper reviews published in England between the turn of the 20th century and the eve of World War Ⅱ, at a time when newsprint was dirt-cheap and stylish arts criticism was considered an ornament to the publications in which it appeared. In those far-off days, it was taken for granted that the critics of major papers would write in detail and at length about the events they covered. Theirs was a serious business, and even those reviewers who wore their learning lightly, like George Bernard Shaw and Ernest Newman, could be trusted to know what they were about. These men believed in journalism as a calling, and were proud to be published in the daily press. “So few authors have brains enough or literary gift enough to keep their own end up in journalism,” Newman wrote, “that I am tempted to define ‘journalism’ as ‘a term of contempt applied by writers who are not read to writers who are’ .”Unfortunately, these critics are virtually forgotten. Neville Cardus, who wrote for the Manchester Guardian from 1917 until shortly before his death in 1975, is now known solely as a writer of essays on the game of cricket. During his lifetime, though, he was also one of England’s foremost classical-music critics, and a stylist so widely admired that his Autobiography (1947) became a best-seller. He was knighted in 1967, the first music critic to be so honored. Yet only one of his books is now in print, and his vast body of writings on music is unknown save to specialists.Is there any chance that Cardus’s criticism will enjoy a revival? The prospect seems remote. Journalistic tastes had changed long before his death, and postmodern readers have little use for the richly upholstered Vicwardian prose in which he specialized. Moreover, the amateur tradition in music criticism has been in headlong retreat.74. It is indicated in Paragraphs 1 and 2 that __________.A. arts criticism has disappeared from big-city newspapers.B. English-language .newspapers used to carry more arts reviews.C. high-quality newspapers retain a large body of readers.D. young readers doubt the suitability of criticism on dailies.75. Newspaper reviews in England before World War Ⅱ were characterized by __________.A. free themes.B. casual style.C. elaborate layout.D. radical viewpoints.76. Which of the following would Shaw and Newman most probably agree on?A. It is writers’ duty to fulfill journalistic goals..B. It is contemptible for writers to be journalists.C. Writers are likely to be tempted into journalism,D. Not all writers are capable of journalistic writing.77. What would be the best title for the text?A. Newspapers of the Good Old DaysB. The Lost Horizon in NewspapersC. Mournful Decline of JournalismD. Prominent Critics in MemoryAir travel has come a long way since that momentous day on 17 Dec.1903, when Wilbur Wright successfully achieved something no one had accomplished—powered flight. However, little did Wilbur and his younger brother Orville know that their invention would create an industry that would enable millions to not only fly 120ft ( as the brothers did ) but thousands of miles.Since then there have been hundreds of commercial airlines that have attempted to make money out of the Wright brothers’ invention. 78 According to Flight Global, there have been 267 airline failure since 2009.79 ,But according to the International Air Transport Association, things may be about to change for the better. ITAT has raised its profit estimate for global carriers to 2.5 billion pounds this year. Although this is still some 50% below last year’s profits, ITAT predicts next year’s total profit could rise to around 4.6 billion. So, could this be a buying opportunity for investors?80 ,They fly aircraft. They sell seats on the aircraft to passengers and capacity for cargo. That’s it. However, hidden beneath the simplicity is operational gearing(经营杠杆）—airlines have to recover high overhead costs before they can make money.That’s why the recession has been so damaging for many under capitalized airlines .Many ran out of money as the economic slowdown cut demands for air travel. Consequently, many airlines were forced to fly their planes even when it was uneconomical to do so. 81 . Low-cost airlines seem to have unlocked the secret of operational gearing by driving ticket prices lower through complicated yield management programs(收益管理项目）that aim to maximize the return.Keys:78-81:B C D (AB)中译英1.在涉及到公司的利益之处，我们永远不会轻易放弃。

数学-高一-上海中学高一上学期周练(11.3)数学试题

上海中学高一周练数学卷2016.11.03一. 填空题1. 求出下列不等式的解集：（1）||0a > （2）2103624x x ≤-+< （3）32x x<- （4）25||60x x -+>（5x <- （6）22110x x x x--+≤（756x <-2. 已知集合8{|1}2A x x =>+，{|||}B x x a b =-≥，若A B R =，A B =∅，则 a = ，b =3. 若函数12y x b =+的图像与以(1,1)A 、(2,3)B 为端点的线段相交，则常数b 的取值范围是4.在maths 先生的数学班的所有学生中，对于问题“你喜欢数学吗？”在学年开始时，有 50%回答“是”，有50%回答“不”，学年结束时，有70%回答“是”，有30%回答“不”，在全部学生中，有x %的学生在学年开始和结束时给出了不同的回答，则x 的最大值和最小值的差是5. 对任意正数x 和y ，不等式1()()9a x y x y++≥恒成立，则常数a 的取值范围是 6. 令,,,a b c d 是集合{3,2,2,4}--中的不同的元素，则22()()a b c d +++的最大值与最小值之差为7. 关于x 的方程2(2)210x m x m +-+-=有一个根属于(0,1)，则m 取值范围是8. 若||2m ≤时不等式2210mx x m -+-<恒成立，则x 的取值范围是9. 若关于x 的不等式组22202(25)50x x x a x a ⎧--≥⎪⎨+++≤⎪⎩的解集中有且仅有两个整数，则a 的取值范围是10. 函数42321x y x =+的最小值是11. 若正实数a 和b 满足5a b +=的最大值是二. 选择题1.“0.53k <<”是“关于x 的不等式4288(2)50x k x k +-+->的解集为R ”的（）A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件2. 若面积为S 的正三角形其外接圆的半径是r ，则（）A. 2S =B. 2S =C. 2S r =D. 2S = 3. 已知集合{|||1}A x x =<，对任意的a A ∈，B A ∈，则1a b ab ++和1a b ab--（） A. 一定都属于A B. 至少有一个属于A C. 至多有一个属于A D.是否属于A 不能确定三. 解答题1. 解关于x 的不等式2(1)10ax a x -++<；2. 求函数y =的定义域和值域；3. 已知非空集合M R ⊆，定义域为R 的函数1,()0,M x M f x x M ∈⎧=⎨∉⎩，若A 、B 是R 的两个非空真子集，试求函数()1()()()1A B A B f x F x f x f x +=++的值域；4. 列车提速可以提高铁路运输量，但并非列车速度越大，列车的流量Q （单位时间内通过观测点的列车数量）就越大，因为列车运行时，前后两车必须要保持一个“安全间隔”，“安全间隔”与列车的速度v 的平方成正比（比例系数0k为定值，00k >），假设所有的列车长度均为，问：列车车速多大时，列车的流量Q 最大；5. 已知0x y >>y x ->-；参考答案一. 填空题1.（1）(,1)(1,)-∞-+∞ （2）(3,1][4,6)-- （3）(2,)+∞ （4）(,3)(2,2)(3,)-∞--+∞ （5）R （6）{1} （7）36(,)25+∞ 2. 2a =，4b = 3. 1[,2]2 4. 60 5. [4,)+∞ 6. 607. 1(,62-8. 9. (2,1][4,5)- 10. 011.二. 选择题1. A2. C3. A三. 解答题 1. 当0a <，1(,)(1,)x a ∈-∞+∞；当0a =，(1,)x ∈+∞；当01a <<，1(1,)x a∈；当1a =，x ∈∅；当1a >， 1(,1)x a ∈； 2. 定义域：[1,2)(2,)+∞，值域：(,8](0,)-∞-+∞； 3. 2{,1}3； 4. 20v Q l k v=+，v =Q 最大； 5. 略；。

上海中学2016-2017学年高一上学期期中考试数学试卷Word版含解析

2016-2017学年上海中学高一(上)期中数学试卷一.填空题I 设集合A={0, 2, 4, 6, 8, 10} , B={4, 8}，则?A B=________ .2. 已知集合A={x|| x| V2} , B={ - 1 , 0, 1, 2, 3}，贝U A AB= ______ .3. _______________________________________ 若x=1且y=1，贝U x+y=2"的逆否命题是 .4. 若f (x+) =X2+=7，则f (3) = ________ .q5. 不等式x> —的解是6. _________________________________________________________________ 若不等式ax2+ (a+1) x+a v 0对一切x € R恒成立，则a的取值范围是________________________ .7. 不等式(x-3) 2- 2寸&=：八'* 3v 0的解是 __________ .&已知集合A={x| - 6< x w 8}, B={x|x w m}，若A U B M B且A A B^ ?，则m的取值范围是.9. ____________________________________________________________________________不等式(x+y) (—+.：)》25对任意正实数x, y恒成立，则正实数a的最小值为_______________ .10. _______________________________________________ 设a> 0, b> 0，且ab=a+4b+5,则ab 的最小值为_____________________________________________ .II .对于二次函数f (x) =4x - 2 ( p- 2) x - 2p - p+1,若在区间［-1, 1］内至少存在一个数c使得f (c)> 0,则实数p的取值范围是__________ .2 212. 已知a, b为正实数，且a+b=2 ,则一…+ 的最小值为a b+1 —二.选择题13. 不等x|x| v x的解集是( )A . {x| 0v x v 1} B. {x| - 1 v x v 1}C. {x| 0v x v 1}或{x| x v- 1},D. {x| - 1 v x v 0, x> 1}14. 若A? B, A? C, B={0, 1, 2, 3, 4, 5, 6}, C={0, 2, 4, 6, 8, 10}，则这样的A 的个数为( )A. 4B. 15C. 16D. 3221115. 不等式ax2+bx+1 >0的解集是(-万，石)，则a- b=( )A. - 7B. 7C.- 5D. 5216. 已知函数f (x) =x +bx,则b v 0”是f(f (x))的最小值与f(x)的最小值相等”的()A .充分不必要条件B .必要不充分条件C.充分必要条件D .既不充分也不必要条件三.解答题17. 解不等式：(1) | x- 2|+| 2x - 3| v 4;,d € E,证明下列不等式：(1)(a2+b2) (c2+d2)>( ac+bd) 2;2 2 2(2) a +b +c > ab+bc+ca.219. 已知二次函数f (x) =ax +bx+1, a, b€ R,当x= - 1时，函数f (x)取到最小值，且最小值为0;(1 )求f (x )解析式；关于x的方程f (x) =|x+1| - k+3恰有两个不相等的实数解，求实数k的取值范围.220. 设关于x的二次方程px + (p - 1) x+p+1=0有两个不相等的正根，且一根大于另一根的两倍，求p的取值范围.[2]21. 已知二次函数f (x) =ax +bx+c (0),记f[ ](x) =f (f (x)),例：f (x) =x +1,[2] 2 22则f[2](x ) = (f (x) ) 2+ 仁(x2+1) 2+1；2 [ 2](1) f (x ) =x - x，解关于x 的方程 f (x ) =x;记厶=(b - 1) 2- 4ac,若f[2](x ) =x有四个不相等的实数根，求△的取值范围.22016-20仃学年上海中学高一（上）期中数学试卷参考答案与试题解析一.填空题1. （2016 秋？徐汇区校级期中）设集合A={0, 2, 4，6，8，10}，B={4，8}，则?A B= {0，2，6，10}.【考点】补集及其运算.【专题】集合思想；定义法；集合.【分析】根据补集的定义进行计算即可.【解答】解：集合A={0，2，4，6，8，10}，B={4，8}，所以?A B={0，2，6，10}.故答案为：{0，2，6，10}.【点评】本题考查了补集的定义与应用问题，是基础题目.2. （2016 秋？徐汇区校级期中）已知集合A={x|| x| V 2}，B={ - 1，0，1，2，3}，则A A B= { - 1，0，1}.【考点】交集及其运算.【专题】计算题；集合思想；定义法；集合.【分析】通过求解绝对值不等式化简集合A，然后直接利用交集运算求解.【解答】解：••• A={x|| x| V 2}={x| - 2V x v2}，B={ - 1, 0，1，2, 3}，••• A A B={ - 1，0，1}，故答案为：{ - 1，0，1}【点评】本题考查绝对值不等式的解法，以及求两个集合的交集的方法. 33（2016秋？徐汇区校级期中）若x=1且y=1，则x+y=2”的逆否命题是若x+y工2，则x 丰1，或护1 ”.【考点】四种命题.【专题】定义法；简易逻辑.【分析】根据已知中的原命题及逆否命题的定义，可得答案.【解答】解：若x=1且y=1，则x+y=2"的逆否命题是若x+y M 2，则x丰1，或y丰1”，故答案为：若x+y M 2，则x M 1，或y M 1”【点评】本题考查的知识点是四种命题，熟练掌握逆否命题的定义，是解答的关键.f (x< ) =X2+~7，则f (3)【考点】函数的值；函数解析式的求解及常用方法.【专题】计算题；配方法；函数的性质及应用.【分析】求出函数的解析式，然后求解函数值即可.1 2丄 1 2【解答】解：f （x+—）=x2+ 2= （x+—）- 2，X K X 所以f (x) =x - 2，则f (3) =7 .故答案为：7.【点评】本题考查函数的解析式的求法，函数值的求法，考查计算能力.5. ( 2016秋？徐汇区校级期中)不等式x>2的解是(-3, 0)U( 3, +〜.x【考点】其他不等式的解法.【专题】计算题；转化思想；综合法；集合.【分析】首先通分化简分式不等式，最后化简为整式不等式，利用穿根法解答即可.宀g【解答】解：原不等式等价于——>0等价于(x+3) (x - 3) x> 0,x由穿根法得到不等式的解集为(- 3, 0)U( 3, +R);故答案为：(-3, 0)U( 3, +8);【点评】本题考查了分式不等式的解法；关键是转化为整式不等式解之；运用穿根法使得解集易得.26. ( 2016秋？徐汇区校级期中)若不等式ax + (a+1) x+a v 0对一切x € R恒成立，则a的取值范围是(-a,- —) _______ .【考点】函数恒成立问题；二次函数的性质.【专题】转化思想；转化法；函数的性质及应用.fa<02【分析】若不等式ax+( a+1) x+av 0对一切x € R恒成立，则［△如1)一纭込,解得a的取值范围.【解答】解：若不等式ax2+ (a+1) x+a v 0对一切x€ R恒成立, fa<0贝［△二(fl 严-4a2<0?解得：a€(- 8,故答案为：(-8,2【点评】本题考查的知识点是函数恒成立问题，二次函数的图象和性质，转化思想，难度中档. 77(2016秋？徐汇区校级期中)不等式(x - 3) 2- 2「：: - 3v 0的解是(0, 6) 【考点】其他不等式的解法.【专题】计算题；转化思想；综合法.【分析】设寸〔汀3严=t，则原不等式化为t2- 2t- 3v 0, (t> 0),解关于t的不等式，然后解出x范围.【解答】解：设「一： =，则原不等式化为t 2- 2t - 3v 0, （t >0）, 所以 t € [0, 3）,即孤-3严[0, 3）,所以（x - 3） 2< 9,解得-3 v x - 3< 3，所以 0v x v 6, 故原不等式的解集为（0, 6）; 故答案为：（0, 6）.【点评】本题考查了利用换元法解不等式；属于基础题.& （ 2016秋？徐汇区校级期中）已知集合 A={x| - 6W x < 8} , B={x|x w m}，若A U B 丰B 且 A AB 丰?，贝U m 的取值范围是 [-6, 81 . 【考点】交集及其运算.【专题】集合思想；转化法；集合.【分析】根据集合的并集和集合的交集得到关于 m 的不等式组，解出即可.【解答】解：A={x| - 6<x < 8}, B={x| x <m}, 若A U B 工B 且A AB 工?,故答案为：[-6, 8].【点评】本题考查了集合的交集、并集的定义，是一道基础题.99 （ 2016秋？徐汇区校级期中）不等式（x+y ）（— +.：）》25对任意正实数x , y 恒成立，则正实数a 的最小值为16 .基本不等式在最值问题中的应用. 转化思想；转化法；不等式.【考点】【专【分析】利用基本不等式进行求解，先求出（ x+y ））的最小值为（9吕.+1） 2,然后2解不等式即可.a+ _y•••（_ 一 + 1） 2> 25,即.一 + 1 > 5, 则时心4, 则 a >16,即正实数a 的最小值为16, 故答案为：16.【点评】本题主要考查基本不等式的应用，利用基本不等式先求出( x+y )「)的最小值为(.「+1) 2是解决本题的关键.10. (2016秋？徐汇区校级期中)设 a >0, b >0，且ab=a+4b+5，则ab 的最小值为 25 . 【考点】基本不等式.【专题】计算题；转化思想；综合法；不等式.【分析】利用基本不等式可将 ab=a+4b+5转化为ab 的不等式，求解不等式可得ab 的最小值. 【解答】解：I a > 0, b > 0,••• a+4b+5=ab ,可得ab >5+2 '4... =5+4...',-.：-，当且仅当a=4b 时取等号. •(叮」」+1)(叮丄—5) > 0, •5或1 (舍去).• ab > 25.故ab 的最小值为将25; 故答案为：25.【点评】本题考查基本不等式，将 2ab=a+b+12转化为不等式是关键，考查等价转化思想与方程思想，属于中档2 211. (2012?天宁区校级模拟)对于二次函数 f (x ) =4x - 2 (p - 2) x -2p - p+1，若在区间［-1 , 1］内至少存在一个数 c 使得f ( c )> 0,则实数p 的取值范围是 (-3,1.5). 【考点】二次函数的性质. 【专题】计算题；转化思想.【分析】由于二次函数f ( x ) =4x 2- 2 ( p - 2) x - 2p 2- p+1的图象是开口方向朝上的抛物2 2线，故二次函数f (x ) =4x - 2( p - 2) x -2p - p+1在区间［-1, 1］内至少存在一个实数 c , 使f ( c )> 0的否定为对于区间［-1, 1］内的任意一个x 都有f ( x )< 0，即f (- 1), f ( 1) 均小于等0，由此可以构造一个关于 p 的不等式组，解不等式组即可求出实数 p 的取值范围.【解答】解：二次函数f (x )在区间［-1 , 1］内至少存在一个实数 c ,使f ( c )> 0的否定是：对于区间［-1, 1］内的任意一个x 都有f (X )w 0,ax y若不等式（x+y ）（' ）> 25对任意正实数x , y 恒成立, 的最小值为（O.+1 ） 2, 即（x+y ）（【解答】解：（x+y ）（+a+r > 1+a+ =1+a+2 , . = （\ o +1） 2,•/fdXof(- i)Co4 2 (p _ 2) _2p^ - P+1<0即•c4+2(p-2) -2p2-pH<02p£+3p- 9>0整理得' 口.2p2-p-l>0解得p> ，或p w- 3,•••二次函数在区间［-1, 1］内至少存在一个实数c,3使f (c)> 0的实数p的取值范围是 (-3 —).【点评】本题考查的知识点是一元二次方程的根的分布与系数的关系，其中根据二次函数的图象是开口方向朝上的抛物线，得到对于区间[-1,1]内的任意一个X 都有f (x )< 0时,12. (2014秋？苏州期末)已知a , b 为正实数，且a+b=2，则+ 的最小值为_a b+16+2^2.【考点】函数在某点取得极值的条件；基本不等式. 【专题】导数的综合应用；不等式的解法及应用.【分析】由a,b 为正实数，且a+b=2,变形可得•“ -一= +a+b - 1+， ='' +1=fa b+1 a b+1 a 3-a(a ), 0 v a v 2 •利用导数研究其单调性极值与最值即可得出. 【解答】解：••• a , b 为正实数，且a+b=2 , — ______ :—=a+〔+「T =^+a+b - 1+=1+仁f （ a ）, a b+1 a b+1 ab+1 a 3 - a_ 2]- G J 6 -（&- 6+3血）f （a ）= 「鳥―.令f ( a )> 0，解得<2，此时函数f (a )单调递增；令f'( a )v 0,解得―，此时函数f (a )单调递减.•••当且仅当a=6 - 3 I 时函数f (a )取得极小值即最小值，血・乜)=呼. 故答案为：".：.1【点评】本题考查了利用导数研究其单调性极值与最值，考查了推理能力与计算能力，属于中档题. 二. 选择题13. (2016秋？徐汇区校级期中)不等 x|x| v x 的解集是( )A . {x| 0v x v 1}B . {x| - 1 v x v 1}C . {x| 0v x v 1}或{x| x v- 1},D . {x| - 1 v x v 0, x > 1}【考点】绝对值不等式. 【专题】不等式的解法及应用.【分析】建议修改C 为{x|0v x v 1,或x v- 1}ffdXo-1）＜0 是解答本题的关键.0v a v 2.原不等式即x （|x| - 1）v 0,等价转化为①」/ ，或② 」.•分别求llxl-i<q [Ixl-i>q得①、②的解集，再取并集，即得所求.【解答】解：不等x| x| V X,即X (| x| - 1) < 0,解①可得0<X V 1，解②可得X V- 1 •把①② 的解集取并集，即得原不等式的解集为{x|0< X V 1}或{X| X V- 1},故选C •【点评】本题主要考查绝对值不等式的解法，体现了分类讨论和等价转化的数学思想，属于中档题.14. （2016 秋？徐汇区校级期中）若A? B, A? C, B={0, 1, 2, 3, 4, 5, 6} , C={0, 2,4, 6, 8, 10}，则这样的A的个数为（）A. 4B. 15C. 16D. 32【考点】子集与真子集.【专题】综合题；方程思想；演绎法；集合.【分析】利用A? B , A? C,可得A? （B A C）,求出B A C,即可得出结论.【解答】解：I A? B, A? C,••• A? （B A C）,••• B={0 , 1, 2 , 3 , 4 , 5 , 6} , C={0 , 2 , 4 , 6 , 8 , 10},• B A C={0 , 2 , 4 , 6},• A的个数为16 ,故选C.【点评】本题考查集合的运算与关系，考查学生的计算能力，比较基础.不等式ax2+bx+1 > 0的解集是15. （2016秋？徐汇区校级期中）A. - 7B. 7C.- 5D. 5【考点】其他不等式的解法.【专题】方程思想；转化法；不等式的解法及应用.【分析】根据不等式的解集构造不等式，化简后于已知得不等式对比即可求出a与b的值, 进而求出a- b的值.211【解答】解：由不等式ax4+bx+1> 0的解集是（-寿,y ）,4 2即-6x - x+1 > 0,与ax +bx+1 > 0 对比得：a= - 6 , b= - 1 ,1 1 2构造不等式（x+万）（x-石）V 0,整理得：6x +x - 1V 0 ,贝U a- b= - 6+1= - 5 ,故选：C.【点评】此题考查学生理解不等式解集的意义，会根据解集构造不等式，是一道基础题.216. (2016?浙江)已知函数f (x ) =x +bx ，贝V bv 0”是“(f (x))的最小值与f ( x )的最小值相等”的( A .充分不必要条件B .必要不充分条件C .充分必要条件D •既不充分也不必要条件【考点】必要条件、充分条件与充要条件的判断. 【专题】函数思想；综合法；简易逻辑.【分析】求出f (x )的最小值及极小值点，分别把b v 0”和“(f ( x ))的最小值与f (x )的最小值相等”当做条件，看能否推出另一结论即可判断.u12【解答】解：f (X )的对称轴为x=-耳，f min (x )=-丄.24(1 )若 b v 0，则-—>-谀，•当兰 f (x ) =-£ 时，f (f (x ))取得最小值f (-*)22 2b 2即f (f (x))的最小值与f (x )的最小值相等.••• b v 0”是“(f (x ))的最小值与f (x )的最小值相等”的充分条件. (2)若f (f (x ))的最小值与f ( x )的最小值相等，• b v 0”不是f' (f (x ))的最小值与f (x )的最小值相等”的必要条件. 故选A . 【点评】本题考查了二次函数的性质，简易逻辑关系的推导，属于基础题. 三. 解答题17. (2016秋？徐汇区校级期中)解不等式：(1) | x - 2|+| 2x - 3| V 4; (2)w x .x _ x _ 2【考点】绝对值不等式的解法；其他不等式的解法. 【专题】对应思想；分类法；不等式的解法及应用.【分析】(1)通过讨论x 的范围，求出各个区间上的x 的范围，从而求出不等式的解集即可；(2)通过讨论x 的范围得到x- 1=0或或解出即可.【解答】解：(1) x >2时，x - 2+2x - 3V 4，解得：x V 3,3—V x v 2 时，2 - x+2x - 2v 4,解得：x v 4,则 f min ( X )W — £即—解得xG-1)2G- 2) G+1)解得：-1< x w 0 或 x=1 或 x >2,故不等式的解集是(-1, 0] U {1} U( 2, +R ).【点评】本题考查了解绝对值不等式问题，考查解分式不等式以及分类讨论思想, 档题.18. (2016秋？徐汇区校级期中)已知 a , b , c , d € E ,证明下列不等式： (1) (a 2+b 2) (c 2+d 2)>( ac+bd ) 2;2 2 2(2) a +b +c >ab+bc+ca . 【考点】不等式的证明.【专题】证明题；转化思想；演绎法；不等式. 【分析】(1)根据不等式的左边减去右边化简结果为(ad - bc ) 2> 0,可得不等式成立；(2)从不等式的左边入手，左边对应的代数式的二倍，分别写成两两相加的形式，在三组相加的式子中分别用均值不等式，整理成最简形式，得到右边的 2倍，两边同时除以2,得到结果.2 2 2 2 2 22 22 22 22 2 2 2 2【解答】证明：••- ( a +b ) ( c +d ) - (ac+bd ) = ( a c +a d +b c +b d ) - (a c +2abcd+b d )2=(ad - bc )》0,••( a 2+b 2) (c ?+d 2 )>( ac+bd ) 2 成立； (2) a +b +c(a 2+b 2+c 2+a 2+b 2+c 2)(2ab+2ca+2bc ) =ab+bc+ca .2 2 2• a +b +c > ab+bc+ca .【点评】本题主要考查用比较法证明不等式，考查均值不等式的应用，考查不等式的证明方法，把差变为因式乘积的形式，是解题的关键，属于中档题.219. (2016秋？徐汇区校级期中)已知二次函数 f (x ) =ax +bx+1, a , b € R ,当x= - 1时,函数f (x )取到最小值，且最小值为 0;(1 )求f (x )解析式；x w,2 - x+3 - 2x < 4，解得：x >£,故不等式的解集是:{X|* < x < 3}；••• x -仁04(x _ 2) (x+2)x<0(x- 2) Cx+l)<0是一道中w x ,-2(2)关于x的方程f (x) =| x+1| - k+3恰有两个不相等的实数解，求实数k的取值范围. 【考点】二次函数的性质；根的存在性及根的个数判断.【专题】计算题；函数思想；转化法；函数的性质及应用.【分析】(1)根据函数的对称轴和函数的最值，即可求出函数的解析式，(2)设 |x+1|=t ，t >0,得到 t 2 - t+k - 3=0,由 x 的方程 f (x ) =|x+1| - k+3 恰有两个不相等的实数解，得到关于t 的方程由两个相等的根或有一个正根，解得即可.【解答】解：(1) x= - 1时，函数f (x )取到最小值，且最小值为 0,•••-——=-1, f (- 1) =a - b+1=0, 解得 a=1, b=2,2•f (x ) =x +2x+1,(2) : f (x ) =|x+1| - k+3,2• x +2x+1=| x+1| - k+3, 即(x+1)=|x+1| - k+3,设| x+1| =t , t > 0, •上2 - t+k - 3=0 ,••• x 的方程f (x ) =|x+1| - k+3恰有两个不相等的实数解，•关于t 的方程由两个相等的根或有一个正根，一 1胃故有k 的取值范围为{k|k= ，或k v 3}4【点评】本题考查了二次函数的性质，以及参数的取值范围，关键是换元，属于中档题.220. (2016秋？徐汇区校级期中)设关于 x 的二次方程px + ( p - 1) x+p+1=0有两个不相等的正根，且一根大于另一根的两倍，求 p 的取值范围.【考点】根的存在性及根的个数判断.【专题】计算题；方程思想；定义法；函数的性质及应用. 【分析】根据根与系数的关系和判别式即可求出p 的范围.2【解答】解：关于x 的二次方程px 2+ ( p - 1) x+p+1=0有两个不相等的正根，则厶=(p - 1) 2 - 4p ( p+1) = - 3p 2- 6p+1> 0,解得-1 -' v p v- 1+',• △ =1 - 4 (k - 3) =0,或- rA=l -4(k-3)>0k-3<0当 x 1+x 2=>0, 及 X 1X 2=p+1>0时，方程的两根为正.解之，得0v p v 1.故0v p v-1.由X2>2x1，并注意p>0，得 3 - ：--T-r >1- p > 0,■；［_,综上得P 的取值范围为{P|0< P <y }.【点评】本题考查了一元二次方程根与系数的关系，属于基础题.2[ 2]21. (2016秋？徐汇区校级期中)已知二次函数 f (x ) =ax+bx+c (0),记f (x ) =f (f(x )),例：f (x ) =x 2+1,[2]2 22则 f [2] (x ) = (f (x )) 2+ 仁(x 2+1) 2+1； 2[ 2](1)f (x ) =x - x ，解关于 x 的方程 f (x ) =x ；记厶=(b - 1) 2- 4ac ,若f [2] (x ) =x 有四个不相等的实数根，求△的取值范围.【考点】二次函数的性质；根的存在性及根的个数判断. 【专题】阅读型；函数思想；构造法；函数的性质及应用. 【分析】(1)根据新类型的定义，求解 f [2] (x ),再解方程即可.(2)换元思想，根据新类型的定义： f (f (x )) =x ，令f (x ) -x=t ，则f (x )- t=x , f ( x )2=t+x ，则有：f (t+x ) =f (x ) - t .带入二次函数 f (x ) =ax +bx+c (a ^ 0)，求出 t , t 又是二次函数的值，即 ax 2+bx+c=t 函数必有两个根，△>0.化简可得(b - 1) 2- 4ac 的取值范围.【解答】解：(1)由题意：当 f (x ) =x 2- x 时，则：f [2] (x ) = (x 2- x ) 2-( x 2 - x ) =x 4 c 3-2x +x ；那么：f [2] (x ) =x ;即：x 4 - 2x 3+x=x ；解得：x=0或x=2 .(2 )根据新类型的定义：f (f ( x ) ) =x ，令f (x ) - x=t , 则 f (x ) - t=x , f (x ) =t+x ,22则有：f (t+x ) =f (x ) - t . 即卩 a (t+x ) +b (t+x ) +c=ax +bx+c - t , 2化简可得：at + (2ax+b+1) t=0 ,解得：t=0或t= "Jg/.△ = (b+[ ) 2 _ 4迅+) = (b+1) 2 - 4ac+4 (b+1) = (b - 1) 2 - 4ac - 4a•.•有两个不相同的实数根△> 0.2 2/•( b - 1) - 4ac - 4>0,即(b - 1) - 4ac >4.综上所得厶=(b - 1) - 4ac 的取值范围是(4, +呵.a当t=0时，即ax 2 +bx+c=x ，有两个不相同的实数根，可得( 当t =''':' 时，ax 2+bx+c=x，整理可得:2b - 1) - 4ac > 0. 二汀亠[一,【点评】本题考查了新定义的应用和理解，计算能力！反函数的利用和构造思想. 换元的代换是解决此题的关键.属于难题.4. （2016秋？徐汇区校级期中）若。

高一数学上学期周练10(2021学年)

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上海市２016－2０1７学年高一数学上学期周练１０一. 填空题1。

若函数()|1|2||f x x x a =++-的最小值为５,则实数a =2。

已知()f x 、()g x 分别是定义在R 上的偶函数和奇函数,且32()()1f x g x x x -=++,则(1)(1)f g +=３。

已知()f x 是定义域为R 的偶函数,当0x ≥时，2()4f x x x =-，那么,不等式(2)5f x +<的解集是4. 若实数0a ≠,函数2,1()2,1x a x f x x a x +<⎧=⎨--≥⎩，(1)(1)f a f a -=+，则a =5. 函数2()|2|f x x x t =--在区间[0,3]上的最大值为2,则t =6。

对于函数42()88(2)5f x x k x k =+-+-，若存在0x R ∈使得0()0f x <，则k 的取值范围是7. 函数222231x x y x x ++=++的值域是8。

函数2y x =+的值域是9. 已知整数a 使得关于x 的不等式2230x ax a -+<的解集中有且仅有三个整数,则a 的值为１０. 不等式1|1|||x x -<的解集是1１。

对于函数()f x =若存在两个不相等的实数,a b 使得()3af a =,()3bf b =都成立,则k 的取值范围是12. 若实数,,a b c 满足222870660a bc a b c bc a ⎧--+=⎪⎨++-+=⎪⎩，则a 的取值范围是13. 已知函数2()2||21f x x a x a ax =---+的图像与x 轴有且仅有三个不同的公共点,则 a =１４.()()10x y ky x y ---+≥对任意满足0x y >>的实数,x y 恒成立，则k 的最大值是15。

2016-2017学年上海市上海中学高一上学期期末考数学试卷含详解

上海中学2016学年第一学期高一期末试卷一、填空题（本大题共有12题，满分36分）考生应在答题纸相应編号的空格内直接填写结果，毎填对得3分.1.函数2()lg(31)f x x =+的定义域是__________．2.函数2()(1)f x x x =的反函数为1()f x -=______.3.若幂函数()f x 的图像经过点127,9⎛⎫ ⎪⎝⎭，则该函数解析式为()f x =______.4.若对任意不等于1的正数a ，函数2()3x f x a -=-的图象都过点P ，则点P 的坐标是______.5.已知2()f x ax bx =+是定义在[]3,2a a -上的偶函数，那么=a ______，b =______.6.方程224log (1)log (1)5x x +++=的解集为_________________.7.已知符号函数1,0sgn()0,01,0x x x x >⎧⎪==⎨⎪-<⎩，则函数()()sgn sgn y x x =+的值域为______.8.已知()f x 是定义在R 上的奇函数，当0x <时，2()f x x x =+，则函数()f x 的解析式为()f x =______.9.函数2650.3x x y -+=的单调增区间为______.10.设函数()y f x =存在反函数1()f x -，若满足1()()f x f x -=恒成立，则称()f x 为“自反函数”，如函数()f x x =，()g x b x =-，()(0)kh x k x =≠等都是“自反函数”，试写出一个不同于上述例子的“自反函数”y =______.11.方程2210x x +-=的解可视为函数2y x =+的图像与函数1y x =的图像交点的横坐标，若方程440x ax +-=的各个实根1x ，2x ，L ，(4)k x k 所对应的点4,i i x x ⎛⎫ ⎪⎝⎭(1,2,,)i k = 均在直线y x =的同侧，则实数a 的取值范围是______.12.对于函数()y f x =，若存在定义域D 内某个区间[,]a b ，使得()y f x =在[,]a b 上的值域也是[,]a b ，则称函数()y f x =在定义域D 上封闭.如果函数()(0)1||kxf x k x =≠+在R 上封闭，那么实数k 的取值范围是______.二、选择题（本大题共有4题，满分16分）每题有且仅有一个正确答案，考生应在答题纸的相应编号的空格内填写答案，每题填对得4分，否则一律得零分.13.已知3()1(0)f x ax bx ab =++≠，若(2017)f k =，则(2017)f -=A.k B.k - C.1k - D.2k-14.定义在R 上的函数()y f x =在区间(,2)-∞上是增函数，且函数(2)y f x =+的图像关于直线1x =对称，则（）A.(1)(5)f f <B.(1)(5)f f >C.(1)(5)f f = D.(0)(5)f f =15.汽车的“燃油效率”是指汽车每消耗1升汽油行驶的里程，下图描述了甲、乙、丙三辆汽车在不同速度下的燃油效率情况.下列叙述中正确的是A.消耗1升汽油，乙车最多可行驶5千米B.以相同速度行驶相同路程，三辆车中，甲车消耗汽油最多C.甲车以80千米/小时的速度行驶1小时，消耗10升汽油D.某城市机动车最高限速80千米/小时.相同条件下，在该市用丙车比用乙车更省油16.设函数()22,0log ,0x x f x x x ⎧+≤⎪=⎨⎪⎩,若关于x 的方程()f x a =有四个不同的解1234,,,x x x x ,且1234x x x x <<<,则()3122341x x x x x ++的取值范围是（）A.()3,∞-+ B.(),3-∞ C.[)3,3- D.(]3,3-三、解答题（本大题共有5题，满分48分）解答下列各题必须在答题纸相应編号的相应区域內写出必要的步骤.17.在平面直角坐标系中，作出下列函数的图像.（1）13y x =；（2）||112x y ⎛⎫=- ⎪⎝⎭.18.已知集合{}226|310330,xx D x x +=-⋅+∈R ，求函数2()log ()22x f x x =⋅∈D 的值域.19.设函数()x xf x ka a -=-（a>0且a≠1）是奇函数．（1）求常数k 的值；（2）若已知f （1）=，且函数22()2()x x g x a a mf x -=+-在区间[1，+∞]）上的最小值为—2，求实数m 的值．20.已知函数()||1m f x x x=+-.（1）当2m =时，判断()f x 在(,0)-∞上的单调性并证明；（2）若对任意x R ∈，不等式(2)0x f >恒成立，求m 的取值范围；（3）讨论函数()y f x =的零点个数.21.已知a ∈R ，函数2()log [(3)34]f x a x a =-+-.（1）当2a =时，解不等式10f x ⎛⎫<⎪⎝⎭；（2）若函数()24y f x x =-的值域为R ，求a 的取值范围；（3）若关于x 的方程21()log 20f x a x ⎛⎫-+=⎪⎝⎭的解集中恰好只有一个元素，求a 的取值范围.上海中学2016学年第一学期高一期末试卷一、填空题（本大题共有12题，满分36分）考生应在答题纸相应編号的空格内直接填写结果，毎填对得3分.1.函数2()lg(31)f x x =+的定义域是__________．【答案】1,13⎛⎫- ⎪⎝⎭【分析】根据函数的解析式，列出使解析式有意义的不等式组，求出解集即可．【详解】要使函数()f x=()2lg 31x +有意义,则10310x x ->⎧⎨+>⎩,解得113x -<<,即函数()f x()2lg 31x +的定义域为1,13⎛⎫- ⎪⎝⎭.故答案为1,13⎛⎫- ⎪⎝⎭．【点睛】本题考查了根据函数解析式求定义域的应用问题，是基础题目．2.函数2()(1)f x x x =的反函数为1()fx -=______.1)x ≥【分析】由2y x =解出x =再交换,x y 的位置,注明定义域即可得到反函数.【详解】由2y x =且1x ≥得x =,所以1()1)f x x -=≥.故答案为1)x ≥.【点睛】本题考查了求反函数,属于基础题.3.若幂函数()f x 的图像经过点127,9⎛⎫ ⎪⎝⎭，则该函数解析式为()f x =______.【答案】23x -【分析】设幂函数()f x x α=,由1(27)9f =可解得.【详解】设幂函数()f x x α=,依题意可得1(27)9f =,所以1279α=,解得23α=-.所以()f x =23x -.故答案为:23x -【点睛】本题考查了幂函数的解析式,属于基础题.4.若对任意不等于1的正数a ，函数2()3x f x a -=-的图象都过点P ，则点P 的坐标是______.【答案】()2,2-【分析】根据指数函数x y a =的图象恒过定点(0,1)以及图象的平移变换可得答案.【详解】因为函数x y a =的图象恒过定点(0,1),所以将函数x y a =的图象向右平移2个单位,向下平移3个单位后所得函数23x y a -=-的图象恒过定点(2,2)-,所以点P 的坐标为(2,2)-.故答案为:(2,2)-.【点睛】本题考查了指数型函数过定点,函数图象的平移变换,属于基础题.5.已知2()f x ax bx =+是定义在[]3,2a a -上的偶函数，那么=a ______，b =______.【答案】①.1②.0【分析】由题可得定义域关于原点O 对称，所以321a a a -=-⇒=，再根据偶函数的定义得0b =.【详解】因为2()f x ax bx =+是定义在[]3,2a a -上的偶函数,所以32a a -=-且()()f x f x -=恒成立,所以1a =,22ax bx ax bx -=+恒成立,所以1a =,20bx =恒成立,所以1,0a b ==.故答案为(1)1;(2)0【点睛】考查了函数奇偶性的定义以及奇偶函数的定义域特征,属于基础题.6.方程224log (1)log (1)5x x +++=的解集为_________________.【答案】{}3【分析】直接利用对数运算公式化简得到答案.【详解】将224log (1)log (1)5x x +++=化简为：2212log (1)log (1)52x x +++=即2log (1)2,3x x +==故答案为{}3【点睛】本题考查了对数方程，属于简单题型.7.已知符号函数1,0sgn()0,01,0x x x x >⎧⎪==⎨⎪-<⎩，则函数()()sgn sgn y x x =+的值域为______.【答案】{}0,2【分析】分三段求出各段的值域,再相并即可得到答案.【详解】当0x >时,sgn()|sgn()|112y x x =+=+=,当0x =时,sgn()|sgn()|000y x x =+=+=,当0x <时,sgn()|sgn()|1|1|2y x x =-+=+-=,所以函数()()sgn sgn y x x =+的值域为:{0,2}.故答案为{0,2}.【点睛】本题考查了分段函数的值域,属于基础题.8.已知()f x 是定义在R 上的奇函数，当0x <时，2()f x x x =+，则函数()f x 的解析式为()f x =______.【答案】22,0,0x x x x x x ⎧-+≥⎨+<⎩【分析】根据()f x 为奇函数,求出0x =,0x >的解析式后,可得分段函数()f x 的解析式.【详解】因为()f x 是定义在R 上的奇函数,所以()()f x f x -=-,当0x =时,(0)(0)f f =-,所以(0)0f =,当0x >时,222()()[()()]()f x f x x x x x x x =--=--+-=--=-+,所以()f x =22,0,0x x x x x x ⎧-+≥⎨+<⎩.故答案为:22,0,0x x x x x x ⎧-+≥⎨+<⎩.【点睛】本题考查了函数的奇函数的性质,分段函数的解析式,属于基础题.9.函数2650.3xx y -+=的单调增区间为______.【答案】(,1]-∞和[3,5].【分析】首先通过函数图象讨论2|65|y x x =-+的递减区间,再根据指数函数0.3x y =递减以及复合函数的同增异减原则可得.【详解】作出函数2|65|y x x =-+的图象如图所示:观察函数图象可知,函数2|65|y x x =-+的递增区间为[1,3]和[5,)+∞,递减区间为(,1]-∞和[3,5],因为指数函数0.3x y =在定义域内递减,根据复合函数的同增异减原则可得2650.3x x y -+=的递增区间为(,1]-∞和[3,5].故答案为:(,1]-∞和[3,5].【点睛】本题考查了二次函数,指数函数的单调性,复合函数的同增异减原则,属于基础题.10.设函数()y f x =存在反函数1()f x -，若满足1()()f x f x -=恒成立，则称()f x 为“自反函数”，如函数()f x x =，()g x b x =-，()(0)kh x k x=≠等都是“自反函数”，试写出一个不同于上述例子的“自反函数”y =______.【答案】1)x ≤≤【分析】根据题意,只要写出一个满足条件的函数即可,如1)y x =≤≤.【详解】根据题意,设1)y x =≤≤,则221y x =-,所以221x y =-,所以x =(01y ≤≤),交换,x y 得反函数1)y x =≤≤.故答案为:1)x ≤≤.【点睛】本题考查了求反函数的解析式,属于基础题.11.方程2210x x +-=的解可视为函数2y x =+的图像与函数1y x=的图像交点的横坐标，若方程440x ax +-=的各个实根1x ，2x ，L ，(4)k x k 所对应的点4,i i x x ⎛⎫⎪⎝⎭(1,2,,)i k = 均在直线y x =的同侧，则实数a 的取值范围是______.【答案】()(),66,-∞-+∞ 【分析】原方程等价于34x a x +=,分别作出3y x a =+和4y x=的图象,分0a >和a<0讨论,利用数形结合即可得到结论.【详解】因为方程440x ax +-=等价于34x a x+=,原方程的实根是3y x a =+与曲线4y x=的交点的横坐标,曲线3y x a =+是由曲线3y x =纵向平移||a 个单位而得到,若交点4,i i x x ⎛⎫ ⎪⎝⎭(1,2,,)i k = 均在直线y x =的同侧,因y x =与4y x =的交点为(2,2),(2,2)--,所以结合图象可得:3022a x a x >⎧⎪+>-⎨⎪≥-⎩或322a x a x <⎧⎪+<⎨⎪≤⎩恒成立,所以32a x >--在[2,)-+∞上恒成立,或32a x <-+在(,2]-∞上恒成立,所以3max (2)a x >--=3(2)26---=,或33min (2)226a x <-+=-+=-,即实数a 的取值范围是()(),66,-∞-+∞ .故答案为:()(),66,-∞-+∞ .【点睛】本题考查了数形结合思想,等价转化思想,函数与方程,幂函数的图象,属于中档题.12.对于函数()y f x =，若存在定义域D 内某个区间[,]a b ，使得()y f x =在[,]a b 上的值域也是[,]a b ，则称函数()y f x =在定义域D 上封闭.如果函数()(0)1||kxf x k x =≠+在R 上封闭，那么实数k 的取值范围是______.【答案】()(),11,-∞-+∞U 【分析】先用定义证明函数1||x y x =+在[0,)+∞上递增,再根据奇偶性可得函数1||xy x =+在R 上为增函数,然后讨论0k >和0k <可得()f x 的单调性,当0k >时,依题意可得,a b 是1||kxx x =+的两个不同的实数解,由此可解得1k >.当0k <时,依题意可得()()f a bf b a =⎧⎨=⎩,由此可推出1k <-.【详解】.设120x x ≤<,则121221121212(1)(1)11(1)(1)x x x x x x y y x x x x +-+-=-=++++1212(1)(1)x x x x -=++,因为120x x ≤<,所以12y y <,所以函数1||xy x =+在[0,)+∞上递增,又函数1||x y x =+为奇函数,所以函数1||xy x =+在R 上为增函数,当0k >时,函数()1||kx f x x =+为增函数,因为()y f x =在[,]a b 上的值域也是[,]a b ,所以()()f a af b b =⎧⎨=⎩,即11kaa a kb b b⎧=⎪+⎪⎨⎪=⎪+⎩,即,a b 是1||kxx x =+的两个不同的实数解,解得0x =或||1x k =-,由||10x k =->得1k >,当0k <时,()1||kx f x x =+为递减函数,因为()y f x =在[,]a b 上的值域也是[,]a b ,所以()()f a b f b a =⎧⎨=⎩,即11kaba kb ab⎧=⎪+⎪⎨⎪=⎪+⎩,因为0,k a b <<,所以0a b <<,所以ka b abkb a ab =-⎧⎨=+⎩,所以()k a b a b +=+,因为0k <,所以0a b +=,即=-b a ,所以()ka a a a =---,所以1011k a =-<-=-,即1k <-.综上所述:1k <-或1k >.故答案为:()(),11,-∞-+∞U .【点睛】本题考查了对新概念的理解转化能力,函数的单调性,奇偶性,函数的定义域和值域,本题是较难题.二、选择题（本大题共有4题，满分16分）每题有且仅有一个正确答案，考生应在答题纸的相应编号的空格内填写答案，每题填对得4分，否则一律得零分.13.已知3()1(0)f x ax bx ab =++≠，若(2017)f k =，则(2017)f -=A.kB.k -C.1k -D.2k-【答案】D【分析】由(2017)f k =可得3201720171a b k ++=,即3(20172017)1a b k -+=-,将其代入到(2017)f -=3201720171a b --+即可得到答案.【详解】因为3()1(0)f x ax bx ab =++≠,所以3201720171a b k ++=,即3(20172017)1a b k -+=-,所以(2017)f -=3201720171a b --+=3(20172017)1112a b k k -++=-+=-.故选:D.【点睛】本题考查了整体替换法,求函数值,属于基础题.14.定义在R 上的函数()y f x =在区间(,2)-∞上是增函数，且函数(2)y f x =+的图像关于直线1x =对称，则（）A.(1)(5)f f <B.(1)(5)f f >C.(1)(5)f f =D.(0)(5)f f =【答案】C【分析】根据平移变换可得,()y f x =的图像关于直线3x =对称,根据对称性可得答案.【详解】因为(2)y f x =+的图像关于直线1x =对称，所以()y f x =的图像关于直线3x =对称，故(1)(5)f f =.故选:C.【点睛】本题考查了函数的图象的平移变换以及函数的对称性,本题为基础题.15.汽车的“燃油效率”是指汽车每消耗1升汽油行驶的里程，下图描述了甲、乙、丙三辆汽车在不同速度下的燃油效率情况.下列叙述中正确的是A.消耗1升汽油，乙车最多可行驶5千米B.以相同速度行驶相同路程，三辆车中，甲车消耗汽油最多C.甲车以80千米/小时的速度行驶1小时，消耗10升汽油D.某城市机动车最高限速80千米/小时.相同条件下，在该市用丙车比用乙车更省油【答案】D【详解】解：对于A ，由图象可知当速度大于40km /h 时，乙车的燃油效率大于5km /L ，∴当速度大于40km /h 时，消耗1升汽油，乙车的行驶距离大于5km ，故A 错误；对于B ，由图象可知当速度相同时，甲车的燃油效率最高，即当速度相同时，消耗1升汽油，甲车的行驶路程最远，∴以相同速度行驶相同路程，三辆车中，甲车消耗汽油最少，故B 错误；对于C ，由图象可知当速度为80km /h 时，甲车的燃油效率为10km /L ，即甲车行驶10km 时，耗油1升，故行驶1小时，路程为80km ，燃油为8升，故C 错误；对于D ，由图象可知当速度小于80km /h 时，丙车的燃油效率大于乙车的燃油效率，∴用丙车比用乙车更省油，故D 正确故选D ．考点：1、数学建模能力；2、阅读能力及化归思想.16.设函数()22,0log ,0x x f x x x ⎧+≤⎪=⎨⎪⎩,若关于x 的方程()f x a =有四个不同的解1234,,,x x x x ,且1234x x x x <<<,则()3122341x x x x x ++的取值范围是（）A.()3,∞-+ B.(),3-∞ C.[)3,3- D.(]3,3-【答案】D【分析】由题意，根据图象得到12x a +=-，22x a +=，23log x a =-，24log x a =，(02)a <≤，推出312234()2214a a x x x x x ++=-.令2a t =，(]1,4t ∈，而函数2y t t=-.即可求解.【详解】()3122234414422222a a a a a x x x x x --++=-⋅+=-⋅【点睛】方法点睛：已知函数零点个数(方程根的个数)求参数值(取值范围)常用的方法：（1）直接法：直接求解方程得到方程的根，再通过解不等式确定参数范围；（2）分离参数法：先将参数分离，转化成求函数的值域问题加以解决；（3）数形结合法：先对解析式变形，进而构造两个函数，然后在同一平面直角坐标系中画出函数的图象，利用数形结合的方法求解.三、解答题（本大题共有5题，满分48分）解答下列各题必须在答题纸相应編号的相应区域內写出必要的步骤.17.在平面直角坐标系中，作出下列函数的图像.（1）13y x =；（2）||112x y ⎛⎫=- ⎪⎝⎭.【答案】(1)见解析,(2)见解析【分析】(1)直接作出幂函数的图象;(2)根据图像变换规律将指数函数先关于y 轴对称，再向下平移一个单位即可.【详解】（1）幂函数13y x =的图象如下:（2）先作出1()2x y =的图象,再去掉y 轴左边图象,保留y 轴右边图象,并将y 轴右边图象翻折到左边,然后向下平移一个单位即可得到.图象如下:【点睛】考查了幂函数、指数函数的图像以及图像的变换,本题为基础题.18.已知集合{}226|310330,x x D x x +=-⋅+∈R ，求函数22()log ()22x x f x x =⋅∈D 的值域.【答案】1,04⎡⎤-⎢⎥⎣⎦【分析】首先解指数不等式得到[2,4]D =，再化简函数表达式,换元变成二次函数求值域可得到答案.【详解】由226310330x x +-⋅+,得2(3)9037290x x -⋅+≤,所以(39)(381)0x x --≤,所以9381x ≤≤,所以24x ≤≤.所以[2,4]D =因为22()log [2,4])22x x f x x =⋅∈,所以()()22()log 1log 2y f x x x ==--,令2log t x =，因为[2,4]x ∈,所以t ∈[1,2],则232y t t =-+,t ∈[1,2],所以32t =时,min 14y =-,1t =或2t =时,max 0y =,函数2()log [2,4])22x f x x =⋅∈的值域为1[,0]4-.【点睛】本题考查了指数不等式，对数的运算以及复合函数的值域问题.本题为中档题，19.设函数()x x f x ka a -=-（a>0且a≠1）是奇函数．（1）求常数k 的值；（2）若已知f （1）=，且函数22()2()x x g x a a mf x -=+-在区间[1，+∞]）上的最小值为—2，求实数m 的值．【答案】（1）；（2）．【详解】试卷分析：（1）函数()x x f x ka a -=-的定义域为R ，∵函数()x x f x ka a -=-（a>0且a≠1）是奇函数∴f （0）=k －1=0，∴k=1．（2）∵f （1）=，∴=，解得a=3或∵a>0且a≠1，∴a=3g （x ）=32x +3-2x －2m （3x －3-x ）=（3x －3-x ）2－2m （3x －3-x ）+2（x≥1）令3x －3-x =t （t≥），则y=t 2－2mt+2=（t—m ）2—m 2+2）当m≥时，min y =—m 2+2=－2，解得m=2或m=-2，舍去当m<时，min y =（）2－2m×+2=－2，解得m=∴m=．试卷解析：（1）函数()x x f x ka a -=-的定义域为R∵函数()x x f x ka a -=-（a>0且a≠1）是奇函数∴f （0）=k －1=0∴k=1（2）∵f （1）=∴=，解得a=3或∵a>0且a≠1∴a=3g （x ）=32x +3-2x －2m （3x －3-x ）=（3x －3-x ）2－2m （3x －3-x ）+2（x≥1）令3x －3-x =t （t≥）则y=t 2－2mt+2=（t—m ）2—m 2+2当m≥时，min y =—m 2+2=－2，解得m=2或m=-2，舍去当m<时，min y =（）2－2m×+2=－2，解得m=∴m=考点：指数函数的应用．20.已知函数()||1m f x x x=+-.（1）当2m =时，判断()f x 在(,0)-∞上的单调性并证明；（2）若对任意x R ∈，不等式(2)0x f >恒成立，求m 的取值范围；（3）讨论函数()y f x =的零点个数.【答案】(1)()f x 在(,0)-∞上的单调递减,证明见解析;(2)14m >；(3)见解析.【分析】(1)当2m =时,利用函数单调性的定义可判断()f x 在(,0)-∞上的单调性，并用定义法证明.(2)利用分离参数的方法将不等式(2)0x f >恒成立，化为22(2)x x m >-，然后求最值即可.(3)函数()y f x =的零点个数,即方程||(0)m x x x x =-+≠的实根的个数，可数形结合分析得出答案.【详解】(1)当2m =,0x <时,2()1f x x x=-+-在(,0)-∞单调递减.证明：任取120x x <<，12121222()()1(1)f x f x x x x x -=-+---+-211222()+()x x x x =--=2121122()()+x x x x x x -=-212121+2=()x x x x x x -⋅由120x x <<，有210x x ->，210x x >，所以212121+2()0x x x x x x -⋅>，即12())0(f x f x ->.则12()()f x f x >，所以当2m =时，()f x 在(,0)-∞上的单调递减.(2)不等式(2)0x f >恒成立,即|2|102x x m +->所以22(2)x x m >-在x R ∈上恒成立.而221112(2)=(2)244x x x ---+≤(当12=2x 即=1x -时取得等号)，所以14m >.(3)由()0f x =即||0(0)x x x m x -+=≠,所以22(0)=(0)x x x m x x x x x x ⎧-+>=-+⎨+<⎩,设22(0)g()(0)x x x x x x x ⎧-+>=⎨+<⎩作出函数g()x的图象，如下.由图可知:当14m >或14m <-时，有1个零点;当14m =或0m =或14m =-时，有2个零点;当104m -<<或104m <<时，有3个零点;【点睛】本题考查函数单调性的判断，以及不等式恒成立问题的求解，利用参数分离的方法解决恒成立问题是基本方法,属于中档题.21.已知a ∈R ，函数2()log [(3)34]f x a x a =-+-.（1）当2a =时，解不等式10f x ⎛⎫< ⎪⎝⎭；（2）若函数()24y f x x =-的值域为R ，求a 的取值范围；（3）若关于x 的方程21()log 20f x a x ⎛⎫-+= ⎪⎝⎭的解集中恰好只有一个元素，求a 的取值范围.【答案】（1）1,12⎛⎫ ⎪⎝⎭（2）[8,)+∞（3）{}1,12,32⎛⎤ ⎥⎝⎦【分析】(1)根据对数函数的单调性可解得,注意真数大于零;(2)化简得到22log (3)4(3)34y a x a x a ⎡⎤=---+-⎣⎦的值域为R ，故2(3)4(3)34a x a x a ---+-能够取到一切大于0的实数，由于二次项系数含参，故需要分类讨论，当3a =时，显然不符合题意；故只能3a >，再结合0∆≥即得答案.(3)化简对数方程得到2(3)(4)10a x a x -+--=,在120a x +>的条件下只有一个根，然后分类讨论即可得到答案.【详解】(1)2a =时，不等式10f x ⎛⎫<⎪⎝⎭等价于21o 2(l g )0x +>-,所以1021x <-<,所以112x<<,所以112x <<,所以不等式10f x ⎛⎫<⎪⎝⎭的解集为1(,1)2.(2)因为函数()24y f x x =-的值域为R ,即22log (3)4(3)34y a x a x a ⎡⎤=---+-⎣⎦的值域为R ,故2(3)4(3)34a x a x a ---+-能够取到一切大于0的实数,当3a =时,2(3)4(3)345a x a x a ---+-=,不符合题意;当3a <时,222(3)4(3)34(3)(4)34(3)(2)8a x a x a a x x a a x a ---+-=--+-=--+-8a ≤-不符合题意,当3a >时,根据二次函数的图象和性质可得216(3)4(3)(34)0a a a ∆=----≥,解得8a ≥;综上所述:a 的取值范围是[8,)+∞.(3)关于x 的方程21()log 20f x a x ⎛⎫-+= ⎪⎝⎭的解集中恰好只有一个元素,所以221log [(3)34]log (2)a x a a x -+-=+的解集中恰好只有一个元素,即120a x +>且1(3)342a x a a x-+-=+的解集中恰好只有一个元素,所以2(3)(4)10a x a x -+--=,即[(3)1](1)0a x x --+=,①当3a =时,解得=1x -,此时121650a x+=-+=>,满足题意;②当2a =时,121x x ==-,此时1230a x +=>也满足题意;③当3a ≠且2a ≠时,两根为113x a =-,21x =-,当13x a =-时,由12330a a x +=->得1a >,当=1x -时,由12210a a x +=->得12a >,因为13x a =-和=1x -只能取一个值,所以只能取=1x -,所以330a -≤且210a ->,解得112a <≤.综上所述:a 的取值范围是1(,1]{2,3}2⋃.【点睛】考查了对数不等式，复合函数的值域问题和对数方程的问题.,分类讨论思想,本题为较难题。